Package 'MPV'

Description

Graphs of confidence interval estimates for bias and standard deviation of in bias-corrected local polynomial regression curve estimates.

Usage

BCCIPlot(data, k1=1, k2=2, h, h2, output, g, layout, incl.biasplot, plotdata)

Arguments

Value

A list containing the confidence interval limits, pointwise estimates of bias, standard deviation of bias, curve estimate, standard deviation of curve estimate, and approximate confidence limits for curve estimates. Graphs of the curve estimate confidence limits and the bias confidence limits.

Author(s)

W. John Braun and Wenkai Ma

Description

Confidence interval estimates for bias in local polynomial regression.

Usage

BCLPBias(xy,k1,k2,h,h2,numgrid=401,alpha=.95)

Arguments

Value

A list containing the confidence interval limits, pointwise estimates of bias, standard deviation of bias, curve estimate, standard deviation of curve estimate, and approximate confidence limits for curve estimates and corresponding bias-corrected estimates.

Author(s)

W. John Braun and Wenkai Ma

Description

Graphs of confidence interval estimates for bias and standard deviation of in local polynomial regression curve estimates.

Usage

BiasVarPlot(data, k1=1, k2=2, h, h2, output=FALSE, g, layout=TRUE)

Arguments

Value

A list containing the confidence interval limits, pointwise estimates of bias, standard deviation of bias, curve estimate, standard deviation of curve estimate, and approximate confidence limits for curve estimates. Graphs of the curve estimate confidence limits and the bias confidence limits.

Author(s)

W. John Braun and Wenkai Ma

Description

The BioOxyDemand data frame has 14 rows and 2 columns.

Usage

data(BioOxyDemand)

Format

This data frame contains the following columns:

x

a numeric vector

y

a numeric vector

Source

Devore, J. L. (2000) Probability and Statistics for Engineering and the Sciences (5th ed), Duxbury

Examples

plot(BioOxyDemand)
summary(lm(y ~ x, data = BioOxyDemand))

Description

Systolic and diastolic blood pressure measurement readings were taken on a 56-year-old male over a 39 day period, sometimes in the mornings (AM) and sometimes in the evening (PM). Varying number of replicate measurements were taken at each time point.

Usage

bp

Format

A data frame with 121 observations on the following 4 variables.

TimeofDay

factor with levels AM and PM

Date

numeric

Systolic

numeric

Diastolic

numeric

Examples

require(lattice)
xyplot(Date ~ Diastolic|TimeofDay, groups=cut(Systolic, c(0, 130, 140,
   200)), data = bp, col=c(3, 1, 2), pch=16)
matplot(bp[, c(3, 4)], type="l", lwd=2, ylab="Pressure")
n <- nrow(bp)
abline(v=(1:n)[bp[,1]=="PM"]-.5, col="grey")
abline(v=(1:n)[bp[,1]=="PM"], col="grey")
abline(v=(1:n)[bp[,1]=="PM"]+.5, col="grey")
bp.stk <- stack(bp, c("Systolic", "Diastolic"))
bp.tmp <- rbind(bp[,1:2], bp[,1:2])
bp.stk <- cbind(bp.tmp, bp.stk)
names(bp.stk) <- c("TimeofDay", "Date", "Pressure", "Type")
reps <- NULL
for (j in rle(paste(bp.stk$Date, bp.stk$TimeofDay))$lengths) reps <- c(reps, (1:j))
bp.stk$Rep <- reps
xyplot(Pressure ~ I(Date+Rep/24)|TimeofDay, groups=Type, data = bp.stk, xlab="Date", pch=16)

Description

The cement data frame has 13 rows and 5 columns.

Usage

data(cement)

Format

This data frame contains the following columns:

y

a numeric vector

x1

a numeric vector

x2

a numeric vector

x3

a numeric vector

x4

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(cement)
pairs(cement)

Description

On a university campus there are a number of areas designated for smoking. Outside of those areas, smoking is not permitted. One of the smoking areas is towards the north end of the campus near some parking lots and a large walkway towards one of the residences. Along the walkway, cigarette butts are visible in the nearby grass. Numbers of cigarette butts were counted at various distances from the smoking area in 200x80 square-cm quadrats located just west of the walkway.

Usage

data("cigbutts")

Format

A data frame with 15 observations on the following 2 variables.

distance

distance from gazebo

count

observed number of butts

Description

The earthquake data frame contains measurements of latitude, longitude, focal depth and magnitude for all earthquakes having magnitude greater than 5.8 between 1964 and 1985.

Usage

earthquake

Format

This data frame contains 2178 observations on the following columns:

depth

numeric vector of focal depths.

latitude

latitudinal coordinate.

longitude

longitudinal coordinate.

magnitude

numeric vector of magnitudes.

Source

Jeffrey S. Simonoff (1996), Smoothing Methods in Statistics, Springer-Verlag, New York.

Examples

summary(earthquake)

Description

Rate of spread measurements (inches/s) in each direction: East, West, North and South for each of 31 experimental runs at given slopes, measured over the given time period of each (measured in seconds).

Usage

fires

Format

A data frame with 31 observations on the following 7 variables.

Run

numeric

Slope

numeric: vertical rise divided by horizontal run, inclined from East to West

ROS_E

numeric: rate of spread measured in easterly direction

ROS_W

numeric: rate of spread measured in westerly direction

ROS_S

numeric: rate of spread measured in southerly direction

ROS_N

numeric: rate of spread measured in northerly direction

Time

numeric

Source

Braun, W.J. and Woolford, D.G. (2013) Assessing a stochastic fire spread simulator. Journal of Environmental Informatics. 22:1-12.

Description

Graphical analysis of one-way ANOVA data. It allows visualization of the usual F-test.

Usage

GANOVA(dataset, var.equal=TRUE, type="QQ", center=TRUE, shift=0)

Arguments

Value

A QQ-plot or a histogram and rugplot

Author(s)

W. John Braun and Sarah MacQueen

Source

Braun, W.J. 2013. Naive Analysis of Variance. Journal of Statistics Education.

Description

This data frame contains the average monthly volume of natural gas used in the furnace of a 1600 square foot house located in London, Ontario, for each month from 2006 until 2011. It also contains the average temperature for each month, and a measure of degree days. Insulation was added to the roof on one occasions, the walls were insulated on a second occasion, and the mid-efficiency furnace was replaced with a high-efficiency furnace on a third occasion.

Usage

data("gasdata")

Format

A data frame with 70 observations on the following 9 variables.

month

numeric 1=January, 12=December

degreedays

numeric, Celsius

cubicmetres

total volume of gas used in a month

dailyusage

average amount of gas used per day

temp

average temperature in Celsius

year

numeric

I1

indicator that roof insulation is present

I2

indicator that wasll insulation is present

I3

indicator that high efficiency furnace is present

Description

This function analyzes regression data graphically. It allows visualization of the usual F-test for significance of regression.

Usage

GFplot(X, y, plotIt=TRUE, sortTrt=FALSE, type="hist", includeIntercept=TRUE, labels=FALSE)

Arguments

Value

A QQ-plot or a histogram and rugplot, or a list if plotIt=FALSE

Author(s)

W. John Braun

Source

Braun, W.J. 2013. Regression Analysis and the QR Decomposition. Preprint.

Examples

# Example 1
X <- p4.18[,-4]
y <- p4.18[,4]
GFplot(X, y, type="hist", includeIntercept=FALSE)
title("Evidence of Regression in the Jojoba Oil Data")
# Example 2
set.seed(4571)
Z <- matrix(rnorm(400), ncol=10)
A <- matrix(rnorm(81), ncol=9)
simdata <- data.frame(Z[,1], crossprod(t(Z[,-1]),A))
names(simdata) <- c("y", paste("x", 1:9, sep=""))
GFplot(simdata[,-1], simdata[,1], type="hist", includeIntercept=FALSE)
title("Evidence of Regression in Simulated Data Set")
# Example 3
GFplot(table.b1[,-1], table.b1[,1], type="hist", includeIntercept=FALSE)
title("Evidence of Regression in NFL Data Set")
# An example where stepwise AIC selects the complement
# of the set of variables that are actually in the true model:
X <- pathoeg[,-10]
y <- pathoeg[,10]
par(mfrow=c(2,2))
GFplot(X, y)
GFplot(X, y, sortTrt=TRUE)
GFplot(X, y, type="QQ")
GFplot(X, y, sortTrt=TRUE, type="QQ")
X <- table.b1[,-1]  # NFL data
y <- table.b1[,1]
GFplot(X, y)

Description

This function analyzes regression data graphically. It allows visualization of the usual F-test for significance of regression.

Usage

GRegplot(X, y, sortTrt=FALSE, includeIntercept=TRUE, type="hist")

Arguments

Value

A histogram or dotplot and rugplot

Author(s)

W. John Braun

Source

Braun, W.J. 2014. Visualization of Evidence in Regression Analysis with the QR Decomposition. Preprint.

Examples

# Example 1
X <- p4.18[,-4]
y <- p4.18[,4]
GRegplot(X, y, includeIntercept=FALSE)
title("Evidence of Regression in the Jojoba Oil Data")
# Example 2
set.seed(4571)
Z <- matrix(rnorm(400), ncol=10)
A <- matrix(rnorm(81), ncol=9)
simdata <- data.frame(Z[,1], crossprod(t(Z[,-1]),A))
names(simdata) <- c("y", paste("x", 1:9, sep=""))
GRegplot(simdata[,-1], simdata[,1], includeIntercept=FALSE)
title("Evidence of Regression in Simulated Data Set")
# Example 3
GRegplot(table.b1[,-1], table.b1[,1], includeIntercept=FALSE)
title("Evidence of Regression in NFL Data Set")
# An example where stepwise AIC selects the complement
# of the set of variables that are actually in the true model:
X <- pathoeg[,-10]
y <- pathoeg[,10]
par(mfrow=c(2,1))
GRegplot(X, y)
GRegplot(X, y, sortTrt=TRUE)
X <- table.b1[,-1]  # NFL data
y <- table.b1[,1]
GRegplot(X, y)

Description

Juliet has 28 rows and 9 columns. The data is of the input and output of the Spirit Still "Juliet" from Endless Summer Distillery. It is suggested to split the data by the Batch factor for ease of use.

Usage

Juliet

Format

The data frame contains the following 9 columns.

Batch

a Factor determing how many times the volume has been through the still.

Vol1

Volume in litres, initial

P1

Percent alcohol present, initial

LAA1

Litres Absolute Alcohol initial, Vol1*P1

Vol2

Volume in litres, final

P2

Percent alcohol present, final

LAA2

Litres Absolute Alcohol final, Vol2*P2

Yield

Percent yield obtained, LAA2/LAA1

Date

Character, Date of run

Details

The purpose of this information is to determine the optimal initial volume and percentage. The information is broken down by Batch. A batch factor 1 means that it is the first time the liquid has gone through the spirit still. The first run through the still should have the most loss due to the "heads" and "tails". Literature states that the first run through a spirit still should yield 70 percent. A batch factor 2 means that it is the second time the liquid has gone through the spirit still. A batch factor 3 means that it is the third time or more that the liquid has gone through the spirit still. Each subsequent distillation should result in a higher yield, never to exceed 95 percent.

Source

Charisse Woods, Endless Summer Distillery, (2015).

Examples

summary(Juliet)

#Split apart the Batch factor for easier use.
juliet<-split(Juliet,Juliet$Batch)
juliet1<-juliet$'1'
juliet2<-juliet$'2'
juliet3<-juliet$'3'

plot(LAA1~LAA2,data=Juliet)
plot(LAA1~LAA2,data=juliet1)

Description

The lengthguesses list consists of 2 numeric vectors, one giving the metric-converted length guesses (in feet) of an auditorium whose actual length (in meters) was 13.1m, and the other containing the length guesses of 69 others (in meters).

Usage

data(lengthguesses)

Format

This list contains the following columns:

imperial

a numeric vector of 69 student guesses as to the length of an auditorium using the imperial system, converted to meters.

metric

a numeric vector of 44 student guesses as to the length of an auditorium using the metric system.

Source

Hills, M. and the M345 Course Team (1986) M345 Statistical Methods, Unit 1: Data, distributions and uncertainty, Milton Keynes: The Open University. Tables 2.1 and 2.4.

References

Hand, D.J., Daly, F., Lunn, A.D., McConway, K.J. and Ostrowski, E. (1994) A Handbook of Small Data Sets. Boca Raton: Chapman & Hall/CRC.

Examples

with(lengthguesses, t.test(imperial, metric))

Description

Numbers of aberrant crypt foci (ACF) in each of six cross-sectional regions of the colons of 66 rats subjected to varying doses of the carcinogen azoxymethane (AOM), sacrificed at 3 different times.

Usage

lesions

Format

This data frame contains the following columns:

T

Incubation time factor, levels: 6, 12 and 18 weeks

INJ

Number of injections

SECT

Section of colon, a factor with levels 1 through 6, where 1 denotes the proximal end of the colon and 6 denotes the distal end

RAT

Label for animal within a particular T-INJ factor level combination

ACF.Total

Total number of ACF lesions in a section of a rat's colon

ACF.total.mult

Sum of ACF multiplicities for a section of a rat's colon

id

Identifier for each of the 66 rats.

Source

Ranjana P. Bird, University of Northern British Columbia, Prince George, Canada.

References

E.A. McLellan, A. Medline and R.P. Bird. Dose response and proliferative characteristics of aberrant crypt foci: putative preneoplastic lesions in rat colon. Carcinogenesis, 12(11): 2093-2098, 1991.

Examples

summary(lesions)
ACF.All <- aggregate(ACF.Total ~  id + INJ + T, FUN=sum, data = lesions)
lesions.glm <- glm(ACF.Total ~ INJ * T, data = ACF.All, family=poisson)
summary(lesions.glm)
lesions.qp <- glm(ACF.Total ~ INJ * T, data = ACF.All, family=quasipoisson)
summary(lesions.qp)
lesions.noInt <- glm(ACF.Total ~ INJ + T, data = ACF.All, family=quasipoisson)
summary(lesions.noInt)

Description

Confidence interval estimates for bias in local polynomial regression.

Usage

LPBias(xy,k1,k2,h,h2,numgrid=401,alpha=.95)

Arguments

Value

A list containing the confidence interval limits, pointwise estimates of bias, standard deviation of bias, curve estimate, standard deviation of curve estimate, and approximate confidence limits for curve estimates.

Author(s)

W. John Braun and Wenkai Ma

Description

Noise measurements for 5 samples of motors, each sample based on a different brand of bearing.

Usage

data("motor")

Format

A data frame with 5 columns.

Brand 1

A numeric vector length 6

Brand 2

A numeric vector length 6

Brand 3

A numeric vector length 6

Brand 4

A numeric vector length 6

Brand 5

A numeric vector length 6

Source

Devore, J. and N. Farnum (2005) Applied Statistics for Engineers and Scientists. Thomson.

Description

The noisyimage is a list. The third component is noisy version of the third component of tarimage.

Usage

data(noisyimage)

Format

This list contains the following elements:

x

a numeric vector having 101 elements.

y

a numeric vector having 101 elements.

xy

a numeric matrix having 101 rows and columns

Examples

with(noisyimage, image(x, y, xy))

Description

The oldwash dataframe has 49 rows and 8 columns. The data are from the start up of a wash still considering the amount of time it takes to heat up to a specified temperature and possible influencing factors.

Usage

data("oldwash")

Format

A data frame with 49 observations on the following 8 variables.

Date

character, the date of the run

startT

degrees Celsius, numeric, initial temperature

endT

degrees Celsius, numeric, final temperature

time

in minutes, numeric, amount of time to reach final temperature

Vol

in litres, numeric, amount of liqiud in the tank (max 2000L)

alc

numeric, the percentage of alcohol present in the liquid

who

character, relates to the person who ran the still

batch

factor with levels 1 = first time through, 2 = second time through

Details

The purpose of the wash still is to increase the percentage of alcohol and strip out unwanted particulate. It can take a long time to heat up and this can lead to problems in meeting production time limits.

Source

Charisse Woods, Endless Summer Distillery (2014)

Examples

oldwash.lm<-lm(log(time)~startT+endT+Vol+alc+who+batch,data=oldwash)
summary(oldwash.lm)
par(mfrow=c(2,2))
plot(oldwash.lm)

data2<-subset(oldwash,batch==2)
hist(data2$time)
data1<-subset(oldwash,batch==1)
hist(data1$time)

oldwash.lmc<-lm(time~startT+endT+Vol+alc+who+batch,data=data1)
summary(oldwash.lmc)
plot(oldwash.lmc)

oldwash.lmd<-lm(time~startT+endT+Vol+alc+who+batch,data=data2)
summary(oldwash.lmd)
plot(oldwash.lmd)

Description

The p11.12 data frame has 19 observations on satellite cost.

Usage

data(p11.12)

Format

This data frame contains the following columns:

cost

first-unit satellite cost

x

weight of the electronics suite

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Simpson and Montgomery (1998)

Examples

data(p11.12)
attach(p11.12)
plot(cost~x)
detach(p11.12)

Description

The p11.15 data frame has 9 rows and 2 columns.

Usage

data(p11.15)

Format

This data frame contains the following columns:

x

a numeric vector

y

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Ryan (1997), Stefanski (1991)

Examples

data(p11.15)
plot(p11.15)
attach(p11.15)
lines(lowess(x,y))
detach(p11.15)

Description

The p12.11 data frame has 44 observations on the fraction of active chlorine in a chemical product as a function of time after manufacturing.

Usage

data(p12.11)

Format

This data frame contains the following columns:

xi

time

yi

available chlorine

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p12.11)
plot(p12.11)
lines(lowess(p12.11))

Description

The p12.12 data frame has 18 observations on an chemical experiment. A nonlinear model relating concentration to reaction time and temperature with an additive error is proposed to fit these data.

Usage

data(p12.12)

Format

This data frame contains the following columns:

x1

reaction time (in minutes)

x2

temperature (in degrees Celsius)

y

concentration (in grams/liter)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p12.12)
attach(p12.12)
# fitting the linearized model 
logy.lm <- lm(I(log(y))~I(log(x1))+I(log(x2)))
summary(logy.lm)
plot(logy.lm, which=1)  # checking the residuals
# fitting the nonlinear model
y.nls <- nls(y ~ theta1*I(x1^theta2)*I(x2^theta3), start=list(theta1=.95, 
theta2=.76, theta3=.21))
 summary(y.nls)
 plot(resid(y.nls)~fitted(y.nls)) # checking the residuals

Description

The p12.16 data frame has 26 observations on 5 variables.

Usage

data(p12.16)

Format

This data frame contains the following columns:

Mixture

numeric

x1

numeric

x2

numeric

x3

numeric

y

numeric

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

References

Myers, R. Technometrics, vol. 6, no. 4, 343-356, 1964.

Description

The p12.8 data frame has 14 rows and 2 columns.

Usage

data(p12.8)

Format

This data frame contains the following columns:

x

a numeric vector

y

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p12.8)

Description

The p13.1 data frame has 25 observation on the test-firing results for surface-to-air missiles.

Usage

data(p13.1)

Format

This data frame contains the following columns:

x

target speed (in Knots)

y

hit (=1) or miss (=0)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p13.1)

Description

The p13.16 data frame has 16 rows and 5 columns.

Usage

data(p13.16)

Format

This data frame contains the following columns:

X1

a numeric vector

X2

a numeric vector

X3

a numeric vector

X4

a numeric vector

Y

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p13.16)

Description

The p13.2 data frame has 20 observations on home ownership.

Usage

data(p13.2)

Format

This data frame contains the following columns:

x

family income

y

home ownership (1 = yes, 0 = no)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p13.2)

Description

The p13.20 data frame has 30 rows and 2 columns.

Usage

data(p13.20)

Format

This data frame contains the following columns:

yhat

a numeric vector

resdev

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p13.20)

Description

The p13.3 data frame has 10 observations on the compressive strength of an alloy fastener used in aircraft construction.

Usage

data(p13.3)

Format

This data frame contains the following columns:

x

load (in psi)

n

sample size

r

number failing

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p13.3)

Description

The p13.4 data frame has 11 observations on the effectiveness of a price discount coupon on the purchase of a two-litre beverage.

Usage

data(p13.4)

Format

This data frame contains the following columns:

x

discount

n

sample size

r

number redeemed

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p13.4)

Description

The p13.5 data frame has 20 observations on new automobile purchases.

Usage

data(p13.5)

Format

This data frame contains the following columns:

x1

income

x2

age of oldest vehicle

y

new purchase less than 6 months later (1=yes, 0=no)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p13.5)

Description

The p13.6 data frame has 15 observations on the number of failures of a particular type of valve in a processing unit.

Usage

data(p13.6)

Format

This data frame contains the following columns:

valve

type of valve

numfail

number of failures

months

months

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p13.6)

Description

The p13.7 data frame has 44 observations on the coal mines of the Appalachian region of western Virginia.

Usage

data(p13.7)

Format

This data frame contains the following columns:

y

number of fractures in upper seams of coal mines

x1

inner burden thickness (in feet), shortest distance between seam floor and the lower seam

x2

percent extraction of the lower previously mined seam

x3

lower seam height (in feet)

x4

time that the mine has been in operation (in years)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Myers (1990)

Examples

data(p13.7)

Description

The p14.1 data frame has 15 rows and 3 columns.

Usage

data(p14.1)

Format

This data frame contains the following columns:

x

a numeric vector

y

a numeric vector

time

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p14.1)

Description

The p14.2 data frame has 18 rows and 3 columns.

Usage

data(p14.2)

Format

This data frame contains the following columns:

t

a numeric vector

xt

a numeric vector

yt

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p14.2)

Description

The p15.4 data frame has 40 rows and 4 columns.

Usage

data(p15.4)

Format

This data frame contains the following columns:

x1

a numeric vector

x2

a numeric vector

y

a numeric vector

set

a factor with levels e and p

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p15.4)

Description

The p2.10 data frame has 26 observations on weight and systolic blood pressure for randomly selected males in the 25-30 age group.

Usage

data(p2.10)

Format

This data frame contains the following columns:

weight

in pounds

sysbp

systolic blood pressure

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p2.10)
attach(p2.10)
cor.test(weight, sysbp, method="pearson")  # tests rho=0
                                           # and computes 95% CI for rho
                                           # using Fisher's Z-transform

Description

The p2.12 data frame has 12 observations on the number of pounds of steam used per month at a plant and the average monthly ambient temperature.

Usage

data(p2.12)

Format

This data frame contains the following columns:

temp

ambient temperature (in degrees F)

usage

usage (in thousands of pounds)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p2.12)
attach(p2.12)
usage.lm <- lm(usage ~ temp)
summary(usage.lm)
predict(usage.lm, newdata=data.frame(temp=58), interval="prediction")
detach(p2.12)

Description

The p2.13 data frame has 16 observations on the number of days the ozone levels exceeded 0.2 ppm in the South Coast Air Basin of California for the years 1976 through 1991. It is believed that these levels are related to temperature.

Usage

data(p2.13)

Format

This data frame contains the following columns:

days

number of days ozone levels exceeded 0.2 ppm

index

a seasonal meteorological index giving the seasonal average 850 millibar temperature.

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Davidson, A. (1993) Update on Ozone Trends in California's South Coast Air Basin. Air Waste, 43, 226-227.

Examples

data(p2.13)
attach(p2.13)
plot(days~index, ylim=c(-20,130))
ozone.lm <- lm(days ~ index)
summary(ozone.lm)
# plots of confidence and prediction intervals:
ozone.conf <- predict(ozone.lm, interval="confidence")
lines(sort(index), ozone.conf[order(index),2], col="red")
lines(sort(index), ozone.conf[order(index),3], col="red")
ozone.pred <- predict(ozone.lm, interval="prediction")
lines(sort(index), ozone.pred[order(index),2], col="blue")
lines(sort(index), ozone.pred[order(index),3], col="blue")
detach(p2.13)

Description

The p2.14 data frame has 8 observations on the molar ratio of sebacic acid and the intrinsic viscosity of copolyesters. One is interested in predicting viscosity from the sebacic acid ratio.

Usage

data(p2.14)

Format

This data frame contains the following columns:

ratio

molar ratio

visc

viscosity

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Hsuie, Ma, and Tsai (1995) Separation and Characterizations of Thermotropic Copolyesters of p-Hydroxybenzoic Acid, Sebacic Acid and Hydroquinone. Journal of Applied Polymer Science, 56, 471-476.

Examples

data(p2.14)
attach(p2.14)
plot(p2.14, pch=16, ylim=c(0,1))
visc.lm <- lm(visc ~ ratio)
summary(visc.lm)
visc.conf <- predict(visc.lm, interval="confidence")
lines(ratio, visc.conf[,2], col="red")
lines(ratio, visc.conf[,3], col="red")
visc.pred <- predict(visc.lm, interval="prediction")
lines(ratio, visc.pred[,2], col="blue")
lines(ratio, visc.pred[,3], col="blue")
detach(p2.14)

Description

The p2.15 data frame has 8 observations on the impact of temperature on the viscosity of toluene-tetralin blends. This particular data set deals with blends with a 0.4 molar fraction of toluene.

Usage

data(p2.15)

Format

This data frame contains the following columns:

temp

temperature (in degrees Celsius)

visc

viscosity (mPa s)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Byers and Williams (1987) Viscosities of Binary and Ternary Mixtures of Polynomatic Hydrocarbons. Journal of Chemical and Engineering Data, 32, 349-354.

Examples

data(p2.15)
attach(p2.15)
plot(visc ~ temp, pch=16)
visc.lm <- lm(visc ~ temp)
plot(visc.lm, which=1)
detach(p2.15)

Description

The p2.16 data frame has 33 observations on the pressure in a tank the volume of liquid.

Usage

data(p2.16)

Format

This data frame contains the following columns:

volume

volume of liquid

pressure

pressure in the tank

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Carroll and Spiegelman (1986) The Effects of Ignoring Small Measurement Errors in Precision Instrument Calibration. Journal of Quality Technology, 18, 170-173.

Examples

data(p2.16)
attach(p2.16)
plot(pressure ~ volume, pch=16)
pressure.lm <- lm(pressure ~ volume)
plot(pressure.lm, which=1)
summary(pressure.lm)
detach(p2.16)

Description

The p2.17 data frame has 17 observations on the boiling point of water (in Fahrenheit degrees) for various barometric pressures (in inches of mercury).

Usage

data(p2.17)

Format

This data frame contains the following columns:

BoilingPoint

numeric vector

BarometricPressure

numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

References

Atkinson, A.C. (1985) Plots, Transformations and Regression, Clarendon Press, Oxford.

Examples

data(p2.17)
attach(p2.17)
plot(BoilingPoint ~ BarometricPressure, pch=16)
detach(p2.17)

Description

The p2.18 data frame has 21 observations on the advertising expenses (in millions of US dollars) and retain impressions (in millions per week) for various companies.

Usage

data(p2.18)

Format

This data frame contains the following columns:

Firm

character vector

Amount.Spent

numeric vector

Returned.Impressions

numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

data(p2.18)
attach(p2.18)
plot(Returned.Impressions ~ Amount.Spent, pch=16)
detach(p2.18)

Description

The p2.7 data frame has 20 observations on the purity of oxygen produced by a fractionation process. It is thought that oxygen purity is related to the percentage of hydrocarbons in the main condensor of the processing unit.

Usage

data(p2.7)

Format

This data frame contains the following columns:

purity

oxygen purity (percentage)

hydro

hydrocarbon (percentage)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p2.7)
attach(p2.7)
purity.lm <- lm(purity ~ hydro)
summary(purity.lm)
# confidence interval for mean purity at 1% hydrocarbon:
predict(purity.lm,newdata=data.frame(hydro = 1.00),interval="confidence")
detach(p2.7)

Description

The p2.9 data frame has 25 rows and 2 columns. See help on softdrink for details.

Usage

data(p2.9)

Format

This data frame contains the following columns:

y

a numeric vector: time

x

a numeric vector: cases stocked

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p2.9)

Description

The p4.18 data frame has 13 observations on an experiment to produce a synthetic analogue to jojoba oil.

Usage

data(p4.18)

Format

This data frame contains the following columns:

x1

reaction temperature

x2

initial amount of catalyst

x3

pressure

y

yield

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Coteron, Sanchez, Matinez, and Aracil (1993) Optimization of the Synthesis of an Analogue of Jojoba Oil Using a Fully Central Composite Design. Canadian Journal of Chemical Engineering.

Examples

data(p4.18)
y.lm <- lm(y ~ x1 + x2 + x3, data=p4.18)
summary(y.lm)
y.lm <- lm(y ~ x1, data=p4.18)

Description

The p4.19 data frame has 14 observations on a designed experiment studying the relationship between abrasion index for a tire tread compound and three factors.

Usage

data(p4.19)

Format

This data frame contains the following columns:

x1

hydrated silica level

x2

silane coupling agent level

x3

sulfur level

y

abrasion index for a tire tread compound

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Derringer and Suich (1980) Simultaneous Optimization of Several Response Variables. Journal of Quality Technology.

Examples

data(p4.19)
attach(p4.19)
y.lm <- lm(y ~ x1 + x2 + x3)
summary(y.lm)
plot(y.lm, which=1)
y.lm <- lm(y ~ x1)
detach(p4.19)

Description

The p4.20 data frame has 26 observations on a designed experiment to determine the influence of five factors on the whiteness of rayon.

Usage

data(p4.20)

Format

This data frame contains the following columns:

acidtemp

acid bath temperature

acidconc

cascade acid concentration

watertemp

water temperature

sulfconc

sulfide concentration

amtbl

amount of chlorine bleach

y

a measure of the whiteness of rayon

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Myers and Montgomery (1995) Response Surface Methodology, pp. 267-268.

Examples

data(p4.20)
y.lm <- lm(y ~ acidtemp, data=p4.20)
summary(y.lm)

Description

The p5.1 data frame has 8 observations on the impact of temperature on the viscosity of toluene-tetralin blends.

Usage

data(p5.1)

Format

This data frame contains the following columns:

temp

temperature

visc

viscosity

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Byers and Williams (1987) Viscosities of Binary and Ternary Mixtures of Polyaromatic Hydrocarbons. Journal of Chemical and Engineering Data, 32, 349-354.

Examples

data(p5.1)
plot(p5.1)

Description

The p5.10 data frame has 27 observations on the effect of three factors on a printing machine's ability to apply coloring inks on package labels.

Usage

data(p5.10)

Format

This data frame contains the following columns:

x1

speed

x2

pressure

x3

distance

yi1

response 1

yi2

response 2

yi3

response 3

ybar.i

average response

si

standard deviation of the 3 responses

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p5.10)
attach(p5.10)
y.lm <- lm(ybar.i ~ x1 + x2 + x3)
plot(y.lm, which=1)
detach(p5.10)

Description

The p5.11 data frame has 8 observations on an experiment with a catapult. This data set is used in Exercise 5.13 of the 6th edition of MPV.

Usage

data(p5.11)

Format

This data frame contains the following columns:

x1

hook

x2

arm length

x3

start angle

x4

stop angle

yi1

response 1

yi2

response 2

yi3

response 3

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

See Also

p5.13

Examples

attach(p5.11)
ybar.i <- apply(p5.11[,5:7], 1, mean)
sd.i <- apply(p5.11[,5:7], 1, sd)
y.lm <- lm(ybar.i ~ x1 + x2 + x3 + x4)
plot(y.lm, which=1)
detach(p5.11)

Description

The p5.12 data frame has 27 observations on 3 variables, with responses replicated 3 times. Averages and standard deviations are calculated for each level of the experimental design.

Usage

data(p5.12)

Format

This data frame contains the following columns:

i

numeric, experimental run number

xi

numeric

x2

numeric

x3

numeric

yi1

response 1

yi2

response 2

yi3

response 3

ybari

average of 3 responses at ith level

si

standard deviation of 3 responses at ith level

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

References

Vining, G. and Myers, R. (1990) "Combining Taguchi and Response Surface Philosophies: A Dual Response Approach," Journal of Quality Technology, 22, 15-22.

Examples

y.lm <- lm(ybari ~ xi + x2 + x3, data = p5.12)
plot(y.lm, which=1)

Description

The p5.13 data frame has 8 observations on 4 variables, with responses replicated 3 times.

Usage

data(p5.13)

Format

This data frame contains the following columns:

x1

numeric

x2

numeric

x3

numeric

x4

numeric

y.1

response 1

y.2

response 2

y.3

response 3

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

References

Schubert, K., M. W., Kerber, S. R., Schmidt, and Jones, S.E. (1992) "The catapult problem; enhanced engineering modeling using experimental design," Quality Engineering, 4, 463-473.

Examples

y.lm <- lm(I((y.1+y.2+y.3)/3) ~ x1 + x2 + x3 + x4, data = p5.13)
plot(y.lm, which=1)

Description

The p5.2 data frame has 11 observations on the vapor pressure of water for various temperatures.

Usage

data(p5.2)

Format

This data frame contains the following columns:

temp

temperature (K)

vapor

vapor pressure (mm Hg)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p5.2)
plot(p5.2)

Description

The p5.21 data frame has 4 observations on 2 variables (replicated 4 times).

Usage

data(p5.21)

Format

This data frame contains the following columns:

Mix.Rate

a numeric vector

y1

a numeric vector

y2

a numeric vector

y3

a numeric vector

y4

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

cementStrength <- reshape(p5.21, idvar = "Mix.Rate", varying=list(2:5), 
    direction="long", v.names=c("TensileStrength"))
 rownames(cementStrength) <- NULL
 anova(lm(TensileStrength ~ Mix.Rate*time, data = cementStrength))

Description

The p5.22 data frame has 18 observations on 2 variables.

Usage

data(p5.22)

Format

This data frame contains the following columns:

Temp

a numeric vector

Density

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

anova(lm(Density ~ Temp, data = p5.22))

Description

The p5.23 data frame has 18 observations on 3 variables.

Usage

data(p5.23)

Format

This data frame contains the following columns:

Batch

a character vector

Pressure

a numeric vector

Strength

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

anova(lm(Strength ~ Pressure*Batch, data = p5.23))

Description

The p5.24 data frame has 13 observations on 7 variables.

Usage

data(p5.24)

Format

This data frame contains the following columns:

Location

a character vector

x1

a numeric vector

x2

a numeric vector

x3

a numeric vector

x4

a numeric vector

x5

a numeric vector

y

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

References

French, R.J. and Schultz, J.E. "Water Use Efficiency of Wheat in a Mediterranean-type Environment, I The Relation between Yield, Water Use, and Climate," Australian Journal of Agricultural Research, 35, 743-764, 1984.

Examples

lm(y ~ x1 + x2 + x3 + x4 + x5, data = p5.24)

Description

The p5.3 data frame has 12 observations on the number of bacteria surviving in a canned food product and the number of minutes of exposure to 300 degree Fahrenheit heat.

Usage

data(p5.3)

Format

This data frame contains the following columns:

bact

number of surviving bacteria

min

number of minutes of exposure

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p5.3)
plot(bact~min, data=p5.3)

Description

The p5.4 data frame has 8 observations on 2 variables.

Usage

data(p5.4)

Format

This data frame contains the following columns:

x

a numeric vector

y

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p5.4)
plot(y ~ x, data=p5.4)

Description

The p5.5 data frame has 14 observations on the average number of defects per 10000 bottles due to stones in the bottle wall and the number of weeks since the last furnace overhaul.

Usage

data(p5.5)

Format

This data frame contains the following columns:

defects

a numeric vector

weeks

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p5.5)
defects.lm <- lm(defects~weeks, data=p5.5)
plot(defects.lm, which=1)

Description

The p7.1 data frame has 10 observations on a predictor variable.

Usage

data(p7.1)

Format

This data frame contains the following columns:

x

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p7.1)
attach(p7.1)
x2 <- x^2
detach(p7.1)

Description

The p7.11 data frame has 11 observations on production cost versus production lot size.

Usage

data(p7.11)

Format

This data frame contains the following columns:

x

production lot size

y

average production cost per unit

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p7.11)
plot(y ~ x, data=p7.11)

Description

The p7.13 data frame has 11 observations on production cost versus production lot size. (This data set was for problem 7-11 in the third edition of MPV).

Usage

data(p7.13)

Format

This data frame contains the following columns:

x

production lot size

y

average production cost per unit

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

plot(y ~ x, data=p7.13)

Description

The p7.15 data frame has 6 observations on vapor pressure of water at various temperatures.

Usage

data(p7.15)

Format

This data frame contains the following columns:

y

vapor pressure (mm Hg)

x

temperature (degrees Celsius)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p7.15)
y.lm <- lm(y ~ x, data=p7.15)
plot(y ~ x, data=p7.15)
abline(coef(y.lm))
plot(y.lm, which=1)

Description

The p7.16 data frame has 26 observations on the observed mole fraction solubility of a solute at a constant temperature.

Usage

data(p7.16)

Format

This data frame contains the following columns:

y

negative logarithm of the mole fraction solubility

x1

dispersion partial solubility

x2

dipolar partial solubility

x3

hydrogen bonding Hansen partial solubility

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

(1991) Journal of Pharmaceutical Sciences 80, 971-977.

Examples

data(p7.16)
pairs(p7.16)

Description

The p7.17 data frame has 6 observations on vapor pressure of water at various temperatures. This data set is the same as p7.15 which was used for exercise 7-15 in the third edition of MPV.

Usage

data(p7.17)

Format

This data frame contains the following columns:

y

vapor pressure (mm Hg)

x

temperature (degrees Celsius)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

y.lm <- lm(y ~ x, data=p7.17)
plot(y ~ x, data=p7.17)
abline(coef(y.lm))
plot(y.lm, which=1)

Description

The p7.18 data frame has 26 observations on the observed mole fraction solubility of a solute at a constant temperature. This data set is the same as p7.16 which was for problem 7-16 in the third edition of MPV.

Usage

data(p7.18)

Format

This data frame contains the following columns:

y

negative logarithm of the mole fraction solubility

x1

dispersion partial solubility

x2

dipolar partial solubility

x3

hydrogen bonding Hansen partial solubility

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

(1991) Journal of Pharmaceutical Sciences 80, 971-977.

Examples

pairs(p7.18)

Description

The p7.19 data frame has 10 observations on the concentration of green liquor and paper machine speed from a kraft paper machine.

Usage

data(p7.19)

Format

This data frame contains the following columns:

y

green liquor (g/l)

x

paper machine speed (ft/min)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

(1986) Tappi Journal.

Examples

data(p7.19)
y.lm <- lm(y ~ x + I(x^2), data=p7.19)
summary(y.lm)

Description

The p7.2 data frame has 10 observations on solid-fuel rocket propellant weight loss.

Usage

data(p7.2)

Format

This data frame contains the following columns:

x

months since production

y

weight loss (kg)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p7.2)
y.lm <- lm(y ~ x + I(x^2), data=p7.2)
summary(y.lm)
plot(y ~ x, data=p7.2)

Description

The p7.20 data frame has 10 observations on the concentration of green liquor and paper machine speed from a kraft paper machine.This data set is the same as p7.19 which was used in problem 7.19 of the third edition of MPV.

Usage

data(p7.20)

Format

This data frame contains the following columns:

y

green liquor (g/l)

x

paper machine speed (ft/min)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

References

(1986) Tappi Journal.

Examples

data(p7.20)
y.lm <- lm(y ~ x + I(x^2), data=p7.20)
summary(y.lm)

Description

The p7.4 data frame has 12 observations on two variables.

Usage

data(p7.4)

Format

This data frame contains the following columns:

x

a numeric vector

y

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p7.4)
y.lm <- lm(y ~ x + I(x^2), data = p7.4)
summary(y.lm)

Description

The p7.6 data frame has 12 observations on softdrink carbonation.

Usage

data(p7.6)

Format

This data frame contains the following columns:

y

carbonation

x1

temperature

x2

pressure

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p7.6)
y.lm <- lm(y ~ x1 + I(x1^2) + x2 + I(x2^2) + I(x1*x2), data=p7.6)
summary(y.lm)

Description

The p8.11 data frame has 25 observations on the tensile strength of synthetic fibre used for men's shirts.

Usage

data(p8.11)

Format

This data frame contains the following columns:

y

tensile strength

percent

percentage of cotton

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Montgomery (2001)

Examples

data(p8.11)
y.lm <- lm(y ~ percent, data=p8.11)
model.matrix(y.lm)

Description

The p8.16 data frame has 17 observations on 4 variables.

Usage

data(p8.16)

Format

This data frame contains the following columns:

Location

numeric

INHIBIT

numeric

UVB

numeric

SURFACE

character

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

References

Smith, R. C. et al., "Ozone depletion: Ultraviolet radiation and phytoplankton biology in Antartic waters," Science, 255, 952-957, 1992.

Description

The p8.3 data frame has 25 observations on delivery times taken by a vending machine route driver.

Usage

data(p8.3)

Format

This data frame contains the following columns:

y

delivery time (in minutes)

x1

number of cases of product stocked

x2

distance walked by route driver

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(p8.3)
pairs(p8.3)

Description

The p9.10 data frame has 31 observations on the rut depth of asphalt pavements prepared under different conditions.

Usage

data(p9.10)

Format

This data frame contains the following columns:

y

change in rut depth/million wheel passes (log scale)

x1

viscosity (log scale)

x2

percentage of asphalt in surface course

x3

percentage of asphalt in base course

x4

indicator

x5

percentage of fines in surface course

x6

percentage of voids in surface course

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Gorman and Toman (1966)

Examples

data(p9.10)
pairs(p9.10)

Description

Artificial regression data which causes stepwise regression with AIC to produce a highly non-parsimonious model. The true model used to simulate the data has only one real predictor (x8).

Usage

pathoeg

Format

This data frame contains the following columns:

x1

a numeric vector

x2

a numeric vector

x3

a numeric vector

x4

a numeric vector

x5

a numeric vector

x6

a numeric vector

x7

a numeric vector

x8

a numeric vector

x9

a numeric vector

y

a numeric vector

Description

Computation of Allen's PRESS statistic for an lm object.

Usage

PRESS(x)

Arguments

Value

Allen's PRESS statistic.

Author(s)

W.J. Braun

See Also

lm

Examples

data(p4.18)
attach(p4.18)
y.lm <- lm(y ~ x1 + I(x1^2))
PRESS(y.lm)
detach(p4.18)

Description

This function is used to display the weight of the evidence against null main effects in data coming from a 1 factor design, using a QQ plot. In practice this method is often called via the function GANOVA.

Usage

qqANOVA(x, y, plot.it = TRUE, xlab = deparse(substitute(x)),
    ylab = deparse(substitute(y)), ...)

Arguments

Value

A QQ plot is drawn.

Author(s)

W. John Braun

Description

Overlays a quadratic curve to a fitted quadratic model.

Usage

quadline(lm.obj, ...)

Arguments

Value

The function superimposes a quadratic curve onto an existing scatterplot.

Author(s)

W.J. Braun

See Also

lm

Examples

data(p4.18)
attach(p4.18)
y.lm <- lm(y ~ x1 + I(x1^2))
plot(x1, y)
quadline(y.lm)
detach(p4.18)

Description

This function analyzes regression data graphically. It allows visualization of the usual F-test for significance of regression.

Usage

Qyplot(X, y, plotIt=TRUE, sortTrt=FALSE, type="hist", includeIntercept=TRUE, labels=FALSE)

Arguments

Value

A QQ-plot or a histogram and rugplot, or a list if plotIt=FALSE

Author(s)

W. John Braun

Source

Braun, W.J. 2013. Regression Analysis and the QR Decomposition. Preprint.

Examples

# Example 1
X <- p4.18[,-4]
y <- p4.18[,4]
Qyplot(X, y, type="hist", includeIntercept=FALSE)
title("Evidence of Regression in the Jojoba Oil Data")
# Example 2
set.seed(4571)
Z <- matrix(rnorm(400), ncol=10)
A <- matrix(rnorm(81), ncol=9)
simdata <- data.frame(Z[,1], crossprod(t(Z[,-1]),A))
names(simdata) <- c("y", paste("x", 1:9, sep=""))
Qyplot(simdata[,-1], simdata[,1], type="hist", includeIntercept=FALSE)
title("Evidence of Regression in Simulated Data Set")
# Example 3
Qyplot(table.b1[,-1], table.b1[,1], type="hist", includeIntercept=FALSE)
title("Evidence of Regression in NFL Data Set")
# An example where stepwise AIC selects the complement
# of the set of variables that are actually in the true model:
X <- pathoeg[,-10]
y <- pathoeg[,10]
par(mfrow=c(2,2))
Qyplot(X, y)
Qyplot(X, y, sortTrt=TRUE)
Qyplot(X, y, type="QQ")
Qyplot(X, y, sortTrt=TRUE, type="QQ")
X <- table.b1[,-1]  # NFL data
y <- table.b1[,1]
Qyplot(X, y)

Description

Percentage of radon from water released in showers with orifices of various diameters. Four replicates were obtained, but it should be noted that the temperatures for the replicates (in degrees Celsius) are 21, 30, 38, and 46, respectively. This information should really be accounted for in any serious analysis of the data.

Usage

data("radon")

Format

A data frame with 15 observations on the following 2 variables.

diameter

shower orifice diameter in mm

rep 1

percentage radon released in first run

rep 2

percentage radon released in second run

rep 3

percentage radon released in third run

rep 4

percentage radon released in fourth run

Source

Hazin, C.A. and Eichholz, G.G. (1992) Influence of Water Temperature and Shower Head Orifice Size on the Release of Radon During Showering, Environment International, 18, 363-369.

Description

Observations of heights, widths and diagonal lengths of several rectangular objects, such as books, photographs, and so on were measured. Only the data in MPV versions 1.62 and later can be trusted; there were errors in the third column in previous versions.

Usage

rectangles

Format

A data frame with 51 observations on the following 4 variables.

h

numeric, heights in centimeters

w

numeric, widths in centimeters

d

numeric, diagonal lengths in centimeters

index

numeric, sum of squares of heights and widths

Examples

x <- sqrt(rectangles$index)
y <- rectangles$d
y.lp <- locpoly(x, y, bandwidth=dpill(x,y), degree=1)
plot(y ~ x)  
lines(y.lp, col=2, lty=2)
abline(0,1) # y = x + measurement error
plot(y.lp$y - y.lp$x, type="l", col=2)

Description

Given a sequence of pseudorandom numbers, this function constructs a random forest prediction model for successive values, based on previous values up to a given lag. The ability of the random forest model to predict future values is inversely related to the quality of the sequence as an approximation to locally random numbers.

Usage

rftest(u, m=5)

Arguments

Value

Side effect is a two way layout of graphs showing effectiveness of prediction on a training and a testing subset of data. Good predictions indicate a poor quality sequence.

Author(s)

W. John Braun

Examples

x <- runif(200)
    rftest(x, m = 4)

Description

The seismictimings data frame has 504 rows and 3 columns. Thickness of a layer of Alberta substratum as measured by several transects of geophones.

Usage

seismictimings

Format

This data frame contains the following columns:

x

longitudinal coordinate of geophone.

y

latitudinal coordinate of geophone.

z

time for signal to pass through substratum.

Examples

plot(y ~ x, data = seismictimings)

Description

The softdrink data frame has 25 rows and 3 columns.

Usage

data(softdrink)

Format

This data frame contains the following columns:

y

a numeric vector

x1

a numeric vector

x2

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(softdrink)

Description

The solar data frame has 29 rows and 6 columns.

Usage

data(solar)

Format

This data frame contains the following columns:

total.heat.flux

a numeric vector

insolation

a numeric vector

focal.pt.east

a numeric vector

focal.pt.south

a numeric vector

focal.pt.north

a numeric vector

time.of.day

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(solar)

Description

Data on an experiment to remove ketchup stains from white cotton fabric by soaking the stained fabric in one of five substrates for one hour. Remaining stains were scored visually and subjectively according to a 6-point scale (0 = completely clean, 5 = no change) The stain data frame has 15 rows and 2 columns.

Usage

data(stain)

Format

This data frame contains the following columns:

treatment

a factor

response

a numeric vector

Examples

data(stain)

Description

The table.b1 data frame has 28 observations on National Football League 1976 Team Performance.

Usage

data(table.b1)

Format

This data frame contains the following columns:

y

Games won in a 14 game season

x1

Rushing yards

x2

Passing yards

x3

Punting average (yards/punt)

x4

Field Goal Percentage (FGs made/FGs attempted)

x5

Turnover differential (turnovers acquired - turnovers lost)

x6

Penalty yards

x7

Percent rushing (rushing plays/total plays)

x8

Opponents' rushing yards

x9

Opponents' passing yards

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(table.b1)
attach(table.b1)
y.lm <- lm(y ~ x2 + x7 + x8)
summary(y.lm)
# over-all F-test:
y.null <- lm(y ~ 1)
anova(y.null, y.lm)
# partial F-test for x7:
y7.lm <- lm(y ~ x2 + x8)
anova(y7.lm, y.lm)
detach(table.b1)

Description

The table.b10 data frame has 40 observations on kinematic viscosity of a certain solvent system.

Usage

data(table.b10)

Format

This data frame contains the following columns:

x1

Ratio of 2-methoxyethanol to 1,2-dimethoxyethane

x2

Temperature (in degrees Celsius)

y

Kinematic viscosity (.000001 m2/s

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Viscosimetric Studies on 2-Methoxyethanol + 1, 2-Dimethoxyethane Binary Mixtures from -10 to 80C. Canadian Journal of Chemical Engineering, 75, 494-501.

Examples

data(table.b10)
attach(table.b10)
y.lm <- lm(y ~ x1 + x2)
summary(y.lm)
detach(table.b10)

Description

The table.b11 data frame has 38 observations on the quality of Pinot Noir wine.

Usage

data(table.b11)

Format

This data frame contains the following columns:

Clarity

a numeric vector

Aroma

a numeric vector

Body

a numeric vector

Flavor

a numeric vector

Oakiness

a numeric vector

Quality

a numeric vector

Region

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(table.b11)
attach(table.b11)
Quality.lm <- lm(Quality ~ Clarity + Aroma + Body + Flavor + Oakiness + 
factor(Region))
summary(Quality.lm)
detach(table.b11)

Description

The table.b12 data frame has 32 rows and 6 columns.

Usage

data(table.b12)

Format

This data frame contains the following columns:

temp

a numeric vector

soaktime

a numeric vector

soakpct

a numeric vector

difftime

a numeric vector

diffpct

a numeric vector

pitch

a numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(table.b12)

Description

The table.b13 data frame has 40 observations on 7 variables concerning jet turbine engine thrust.

Usage

data(table.b13)

Format

This data frame contains the following columns:

y

a numeric vector representing thrust

x1

a numeric vector representing primary speed of rotation

x2

a numeric vector representing secondary speed of rotation

x3

a numeric vector representing fuel flow rate

x4

a numeric vector representing pressure

x5

a numeric vector representing exhaust temperature

x6

a numeric vector representing ambient temperature at time of test

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(table.b13)

Description

The table.b14 data frame has 25 observations on the transient points of an electronic inverter.

Usage

data(table.b14)

Format

This data frame contains the following columns:

x1

width of the NMOS Device

x2

length of the NMOS Device

x3

width of the PMOS Device

x4

length of the PMOS Device

x5

a numeric vector

y

transient point of PMOS-NMOS Inverters

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(table.b14)
y.lm <- lm(y ~ x1 + x2 + x3 + x4, data=table.b14)
plot(y.lm, which=1)

Description

The table.b15 data frame has 60 observations on the mortality, environment, and demographic variables for a sample of American cities.

Usage

data(table.b15)

Format

This data frame contains the following columns:

City

character vector

Mort

numeric vector, age-adjusted mortality from all causes per 100000

Precip

numeric vector, precipitation in inches

Educ

numeric vector, median number of school years completed

Nonwhite

numeric vector, percentage of 1960 population that is nonwhite

Nox

numeric vector, relative pollution potential of nitrous oxides

SO2

numeric vector, relative pollution potential of sulfur dioxide

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

References

McDonald, G. C. and Ayers, J.A. [1978], "Some applications of Chernuff faces: A technique for graphically representing multivariate data", in Graphical Representation of Multivariate Data, Academic Press, New York.

Examples

data(table.b15)
pairs(table.b15[,-1])

Description

The table.b16 data frame has 38 observations on 6 variables.

Usage

data(table.b16)

Format

This data frame contains the following columns:

Country

character

LifeExp

numeric

People.per.TV

numeric

People.per.Dr

numeric

LifeExpMale

numeric

LifeExpFemale

numeric

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Description

The table.b17 data frame has 25 observations on 5 variables.

Usage

data(table.b17)

Format

This data frame contains the following columns:

Satisfaction

numeric vector

Age

numeric vector

Severity

numeric vector

Surgical.Medical

numeric vector

Anxiety

numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

pairs(table.b17)

Description

The table.b18 data frame has 16 observations on 9 variables.

Usage

data(table.b18)

Format

This data frame contains the following columns:

y

numeric vector

x1

numeric vector

x2

numeric vector

x3

numeric vector

x4

numeric vector

x5

numeric vector

x6

numeric vector

x7

numeric vector

x8

numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

pairs(table.b18)

Description

The table.b19 data frame has 32 observations on 11 variables.

Usage

data(table.b19)

Format

This data frame contains the following columns:

y

numeric vector

x1

numeric vector

x2

numeric vector

x3

numeric vector

x4

numeric vector

x5

numeric vector

x6

numeric vector

x7

numeric vector

x8

numeric vector

x9

numeric vector

x10

numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

pairs(table.b19)

Description

The table.b2 data frame contains 29 observations on 6 variables related to a solar thermal energy test.

Usage

data(table.b2)

Format

This data frame contains the following columns:

y

a numeric vector measuring total heat flux (kwatts)

x1

a numeric vector measuring insulation (watts/m^2)

x2

a numeric vector measuring position of focal point in east direction (inches)

x3

a numeric vector measuring position of focal point in south direction (inches)

x4

a numeric vector measuring position of focal point in north direction (inches)

x5

a numeric vector representing time of day

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

data(table.b2)
pairs(table.b2)

Description

The table.b20 data frame has 18 observations on 6 variables.

Usage

data(table.b20)

Format

This data frame contains the following columns:

x1

numeric vector

x2

numeric vector

x3

numeric vector

x4

numeric vector

x5

numeric vector

y

numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

pairs(table.b20)

Description

The table.b22 data frame has 30 observations on 12 variables.

Usage

data(table.b22)

Format

This data frame contains the following columns:

Team

character vector

Wins

numeric vector

Batter.Age

numeric vector

Runs

numeric vector

HRs

numeric vector

SLG

numeric vector

Pitcher.Age

numeric vector

ERA

numeric vector

SO

numeric vector

HRA

numeric vector

RA.G

numeric vector

Errors

numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

pairs(table.b22[,-1])

Description

The table.b23 data frame has 59 observations on 8 variables.

Usage

data(table.b23)

Format

This data frame contains the following columns:

Player

character vector

Per

numeric vector

Lane.Agility.Time..Seconds.

numeric vector

Shuttle.Run..Seconds.

numeric vector

Three.Quarter.Sprint..Seconds.

numeric vector

Standing.Vertical.Leap..Inches.

numeric vector

Max.Vertical.Leap..Inches.

numeric vector

Position

character vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

pairs(table.b23[,-c(1, 8)])

Description

The table.b24 data frame has 51 observations on 6 variables.

Usage

data(table.b24)

Format

This data frame contains the following columns:

City

character vector

Population

numeric vector

X95th.Percentile.Income

numeric vector

Median.Sale.Price

numeric vector

Median.Price.sqft

numeric vector

Rental.Price

numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

pairs(table.b24[,-1])

Description

The table.b25 data frame has 50 observations on 6 variables.

Usage

data(table.b25)

Format

This data frame contains the following columns:

Player

character vector

Average.Score

numeric vector

SG..Off.the.Tee

numeric vector

SG..Approach.to.Green

numeric vector

SG..Around.the.Green

numeric vector

SG..Putting

numeric vector

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2021) Introduction to Linear Regression Analysis. 6th Edition, John Wiley and Sons.

Examples

pairs(table.b25[,-1])

Description

The table.b3 data frame has observations on gasoline mileage performance for 32 different automobiles.

Usage

data(table.b3)

Format

This data frame contains the following columns:

y

Miles/gallon

x1

Displacement (cubic in)

x2

Horsepower (ft-lb)

x3

Torque (ft-lb)

x4

Compression ratio

x5

Rear axle ratio

x6

Carburetor (barrels)

x7

No. of transmission speeds

x8

Overall length (in)

x9

Width (in)

x10

Weight (lb)

x11

Type of transmission (1=automatic, 0=manual)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Motor Trend, 1975

Examples

data(table.b3)
attach(table.b3)
y.lm <- lm(y ~ x1 + x6)
summary(y.lm)
# testing for the significance of the regression:
y.null <- lm(y ~ 1)
anova(y.null, y.lm)
# 95% CI for mean gas mileage:
predict(y.lm, newdata=data.frame(x1=275, x6=2), interval="confidence")
# 95% PI for gas mileage:
predict(y.lm, newdata=data.frame(x1=275, x6=2), interval="prediction")
detach(table.b3)

Description

The table.b4 data frame has 24 observations on property valuation.

Usage

data(table.b4)

Format

This data frame contains the following columns:

y

sale price of the house (in thousands of dollars)

x1

taxes (in thousands of dollars)

x2

number of baths

x3

lot size (in thousands of square feet)

x4

living space (in thousands of square feet)

x5

number of garage stalls

x6

number of rooms

x7

number of bedrooms

x8

age of the home (in years)

x9

number of fireplaces

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Narula, S.C. and Wellington (1980) Prediction, Linear Regression and Minimum Sum of Relative Errors. Technometrics, 19, 1977.

Examples

data(table.b4)
attach(table.b4)
y.lm <- lm(y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9)
summary(y.lm)
detach(table.b4)

Description

The table.b5 data frame has 27 observations on liquefaction.

Usage

data(table.b5)

Format

This data frame contains the following columns:

y

CO2

x1

Space time (in min)

x2

Temperature (in degrees Celsius)

x3

Percent solvation

x4

Oil yield (g/100g MAF)

x5

Coal total

x6

Solvent total

x7

Hydrogen consumption

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

(1978) Belle Ayr Liquefaction Runs with Solvent. Industrial Chemical Process Design Development, 17, 3.

Examples

data(table.b5)
attach(table.b5)
y.lm <- lm(y ~ x6 + x7)
summary(y.lm)
detach(table.b5)

Description

The table.b6 data frame has 28 observations on a tube-flow reactor.

Usage

data(table.b6)

Format

This data frame contains the following columns:

y

Nb0Cl3 concentration (g-mol/l)

x1

COCl2 concentration (g-mol/l)

x2

Space time (s)

x3

Molar density (g-mol/l)

x4

Mole fraction CO2

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

(1972) Kinetics of Chlorination of Niobium oxychloride by Phosgene in a Tube-Flow Reactor. Industrial and Engineering Chemistry, Process Design Development, 11(2).

Examples

data(table.b6)
# Partial Solution to Problem 3.9
attach(table.b6)
y.lm <- lm(y ~ x1 + x4)
summary(y.lm)
detach(table.b6)

Description

The table.b7 data frame has 16 observations on oil extraction from peanuts.

Usage

data(table.b7)

Format

This data frame contains the following columns:

x1

CO2 pressure (bar)

x2

CO2 temperature (in degrees Celsius)

x3

peanut moisture (percent by weight)

x4

CO2 flow rate (L/min)

x5

peanut particle size (mm)

y

total oil yield

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Kilgo, M.B. An Application of Fractional Experimental Designs. Quality Engineering, 1, 19-23.

Examples

data(table.b7)
attach(table.b7)
# partial solution to Problem 3.11:
peanuts.lm <- lm(y ~ x1 + x2 + x3 + x4 + x5)
summary(peanuts.lm)
detach(table.b7)

Description

The table.b8 data frame has 36 observations on Clathrate formation.

Usage

data(table.b8)

Format

This data frame contains the following columns:

x1

Amount of surfactant (mass percentage)

x2

Time (min)

y

Clathrate formation (mass percentage)

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Tanii, T., Minemoto, M., Nakazawa, K., and Ando, Y. Study on a Cool Storage System Using HCFC-14 lb Clathrate. Canadian Journal of Chemical Engineering, 75, 353-360.

Examples

data(table.b8)
attach(table.b8)
clathrate.lm <- lm(y ~ x1 + x2)
summary(clathrate.lm)
detach(table.b8)

Description

The table.b9 data frame has 62 observations on an experimental pressure drop.

Usage

data(table.b9)

Format

This data frame contains the following columns:

x1

Superficial fluid velocity of the gas (cm/s)

x2

Kinematic viscosity

x3

Mesh opening (cm)

x4

Dimensionless number relating superficial fluid velocity of the gas to the superficial fluid velocity of the liquid

y

Dimensionless factor for the pressure drop through a bubble cap

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

References

Liu, C.H., Kan, M., and Chen, B.H. A Correlation of Two-Phase Pressure Drops in Screen-Plate Bubble Column. Canadian Journal of Chemical Engineering, 71, 460-463.

Examples

data(table.b9)
attach(table.b9)
# Partial Solution to Problem 3.13:
y.lm <- lm(y ~ x1 + x2 + x3 + x4)
summary(y.lm)
detach(table.b9)

Description

The table5.2 data frame has 53 observations on energy usage (KWH) and corresponding demand (KW) at a sample of residences. This is the Electric Utility Data of Example 5.1.

Usage

data(table5.2)

Format

This data frame contains the following columns:

Customer

a numeric vector of customer IDs

x

a numeric vector of energy usage values

y

a numeric vector of demand values

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

plot(y ~ x, xlab = "Usage", ylab = "Demand", data = table5.2)
anova(lm(y ~ x, data = table5.2)) # Note the typo in Table 5.3 for SS Regression

Description

The table5.5 data frame has 25 observations on wind velocity (mph) and corresponding DC output from a windmill turbine. This is the Windmill Data of Example 5.2.

Usage

data(table5.5)

Format

This data frame contains the following columns:

v

numeric vector of velocities

DC

numeric vector of DC output values

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

plot(DC ~ v, data = table5.5)

Description

The table5.9 data frame has 30 observations on wind income (dollars) and corresponding advertising expense. This is the Restaurant Food Sales Data of Example 5.5.

Usage

data(table5.9)

Format

This data frame contains the following columns:

y

numeric vector of incomes

x

numeric vector of advertising expenses

Source

Montgomery, D.C., Peck, E.A., and Vining, C.G. (2001) Introduction to Linear Regression Analysis. 3rd Edition, John Wiley and Sons.

Examples

plot(y ~ x, xlab = "expense", ylab = "income", data = table5.9)
# carrying out the calculations in the example to obtain the regression
# weights:
indices <- rep(1:10, c(3, 2, 1, 5, 5, 1, 6, 2, 1, 4))
xbar <- sapply(split(table5.9$x, indices), mean)
yvarhat <- sapply(split(table5.9$y, indices), var)
xbar <- xbar[!is.na(yvarhat)]
yvarhat <- yvarhat[!is.na(yvarhat)]
eg55.lm <- lm(yvarhat ~ xbar)
wts <- 1/predict(eg55.lm, newdata = data.frame(xbar = table5.9$x))
# the values are different from those of the textbook; there seems
# to be some problem with either the calculations or the recorded values

Description

The tarimage is a list. Most of the values are 0, but there are small regions of 1's.

Usage

data(tarimage)

Format

This list contains the following elements:

x

a numeric vector having 101 elements.

y

a numeric vector having 101 elements.

xy

a numeric matrix having 101 rows and columns

Examples

with(tarimage, image(x, y, xy))

Description

This function analyzes regression data graphically. It allows visualization of the usual t-tests for individual regression coefficients.

Usage

tplot(X, y, plotIt=TRUE, type="hist", includeIntercept=TRUE)

Arguments

Value

A QQ-plot or a histogram and rugplot, or a list if plotIt=FALSE

Author(s)

W. John Braun

Examples

# Jojoba oil data set
X <- p4.18[,-4]
y <- p4.18[,4]
tplot(X, y, type="hist", includeIntercept=FALSE)
title("Tests for Individual Coefficients in the Jojoba Oil Regression")
# Simulated data set where none of the predictors are in the true model:
set.seed(4571)
Z <- matrix(rnorm(400), ncol=10)
A <- matrix(rnorm(81), ncol=9)
simdata <- data.frame(Z[,1], crossprod(t(Z[,-1]),A))
names(simdata) <- c("y", paste("x", 1:9, sep=""))
X <- simdata[,-1]
y <- simdata[,1]
tplot(X, y, type="hist", includeIntercept=FALSE)
title("Tests for Individual Coefficients for the Simulated Data Set")
# NFL Data set:
X <- table.b1[,-1]
y <- table.b1[,1]
tplot(X, y, type="hist", includeIntercept=FALSE)
title("Tests for Individual Coefficients for the NFL Data Set")
# Simulated Data set where x8 is the only predictor in the true model:
X <- pathoeg[,-10]
y <- pathoeg[,10]
par(mfrow=c(2,2))
tplot(X, y)
tplot(X, y, type="QQ")

Description

A random sample of observations taken from the 'Loblolly' data frame, one per Seed.

Usage

data("tree.sample")

Format

A data frame with 12 observations on the following 2 variables.

height

tree heights (ft)

age

tree ages (yr)

Description

This function graphically displays the coefficient multipliers used in the Regression Plot for the given predictor.

Usage

Uplot(X.qr, Xcolumn = 1, ...)

Arguments

Value

A bar plot is displayed.

Author(s)

W. John Braun

Examples

# Jojoba oil data set
X <- p4.18[,-4]
Uplot(X, 1:4)
# NFL data set; see GFplot result first
X <- table.b1[,-1]
Uplot(X, c(2,3,9))
# In this example, x8 is the only predictor in
# the true model:
X <- pathoeg[,-10]
y <- pathoeg[,10]
pathoeg.F <- GFplot(X, y, plotIt=FALSE)
Uplot(X, "x8")
Uplot(X, 9) # same as above
Uplot(pathoeg.F$QR, 9) # same as above
X <- table.b1[,-1]
Uplot(X, c("x2", "x3", "x9"))

Description

Measurements in centimeters of the widths of a random collection of books.

Usage

widths

Format

A numeric vector of length 24.

Description

The windWin80 data frame has 366 observations on midnight and noon windspeed at the Winnipeg International Airport for the year 1980.

Usage

data(windWin80)

Format

This data frame contains the following columns:

h0

a numeric vector containing the wind speeds at midnight.

h12

a numeric vector containing the wind spees at the following noon.

Examples

data(windWin80)
ts.plot(windWin80$h12^2)

Description

The Wpgtemp data frame has 7671 observations on daily maximum temperatures at the Winnipeg International Airport for the years 1960 through 1980.

Usage

data(Wpgtemp)

Format

This data frame contains the following columns:

temperature

A numeric vector containing the temperatures in degrees Celsius

day

A numeric vector denoting the observation date in numbers of days after December 31, 1959

Source

Environment Canada

Examples

summary(Wpgtemp)

Description

Daily observations taken from 2012 through 2021 on temperature, rain, snow and wind for Fort Frances, Kenora and Dryden, Ontario.

Usage

wxNWO

Format

A data frame with 10959 observations on the following 31 variables.

Longitude

numeric

Latitude

numeric

Station.Name

character

Climate.ID

numeric

Date.Time

numeric

Year

numeric

Month

numeric

Day

numeric

Data.Quality

numeric

Max.Temp

numeric

Max.Temp.Flag

numeric

Min.Temp

numeric

Min.Temp.Flag

numeric

Mean.Temp

numeric

Mean.Temp.Flag

numeric

Heat.Deg.Days

numeric

Heat.Deg.Days.Flag

numeric

Cool.Deg.Days

numeric

Cool.Deg.Days.Flag

numeric

Total.Rain

numeric

Total.Rain.Flag

numeric

Total.Snow

numeric

Total.Snow.Flag

numeric

Total.Precip

numeric

Total.Precip.Flag

numeric

Snow.on.Ground

numeric

Snow.on.Ground.Flag

numeric

Dir.of.Max.Gust

numeric

Dir.of.Max.Gust.Flag

numeric

Speed.of.Max.Gust

numeric

Speed.of.Max.Gust.Flag

numeric