382 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION(a) Fit a simple linear model relating highway miles per gal-
lon (y) to engine displacement (x) using least squares.
(b) Find an estimate of the mean highway gasoline mileage
performance for a car with 150 cubic inches engine dis-
placement.
(c) Obtain the fitted value of yand the corresponding residual
for a car, the Ford Escort, with engine displacement of 114
cubic inches.
11-8. An article in the Tappi Journal(March, 1986) pre-
sented data on green liquor Na 2 S concentration (in grams per
liter) and paper machine production (in tons per day). The data
(read from a graph) are shown as follows:y 40 42 49 46 44 48x 825 830 890 895 890 910y 46 43 53 52 54 57 58x 915 960 990 1010 1012 1030 1050(a) Fit a simple linear regression model with ygreen liquor
Na 2 S concentration and xproduction. Find an estimate
of ^2. Draw a scatter diagram of the data and the resulting
least squares fitted model.
(b) Find the fitted value of ycorresponding to x910 and
the associated residual.
(c) Find the mean green liquor Na 2 S concentration when the
production rate is 950 tons per day.
11-9. An article in the Journal of Sound and Vibration
(Vol. 151, 1991, pp. 383–394) described a study investigating
the relationship between noise exposure and hypertension.
The following data are representative of those reported in the
article.y 1012514 6 2 3x 60 63 65 70 70 70 80 90 80 80y 5468457 9 7 6x 85 89 90 90 90 90 94 100 100 100(a) Draw a scatter diagram of y(blood pressure rise in
millimeters of mercury) versus x(sound pressure level in
decibels). Does a simple linear regression model seem
reasonable in this situation?
(b) Fit the simple linear regression model using least squares.
Find an estimate of ^2.
(c) Find the predicted mean rise in blood pressure level asso-
ciated with a sound pressure level of 85 decibals.
11-10. An article in Wear(Vol. 152, 1992, pp. 171–181)
presents data on the fretting wear of mild steel and oil viscos-
ity. Representative data follow, with xoil viscosity and y
wear volume ( 10 4 cubic millimeters).(a) Construct a scatter plot of the data. Does a simple linear
regression model appear to be plausible?
(b) Fit the simple linear regression model using least squares.
Find an estimate of ^2.
(c) Predict fretting wear when viscosity x30.
(d) Obtain the fitted value of ywhen x22.0 and calculate
the corresponding residual.
11-11. An article in the Journal of Environmental
Engineering(Vol. 115, No. 3, 1989, pp. 608–619) reported the
results of a study on the occurrence of sodium and chloride in
surface streams in central Rhode Island. The following data
are chloride concentration y(in milligrams per liter) and road-
way area in the watershed x(in percentage).y 4.4 6.6 9.7 10.6 10.8 10.9x 0.19 0.15 0.57 0.70 0.67 0.63y 11.8 12.1 14.3 14.7 15.0 17.3x 0.47 0.70 0.60 0.78 0.81 0.78y 19.2 23.1 27.4 27.7 31.8 39.5x 0.69 1.30 1.05 1.06 1.74 1.62
(a) Draw a scatter diagram of the data. Does a simple linear
regression model seem appropriate here?
(b) Fit the simple linear regression model using the method of
least squares. Find an estimate of ^2.
(c) Estimate the mean chloride concentration for a watershed
that has 1% roadway area.
(d) Find the fitted value corresponding to x0.47 and the
associated residual.
11-12. A rocket motor is manufactured by bonding together
two types of propellants, an igniter and a sustainer. The shear
strength of the bond yis thought to be a linear function of the
age of the propellant xwhen the motor is cast. Twenty obser-
vations are shown in the table on the next page.
(a) Draw a scatter diagram of the data. Does the straight-line
regression model seem to be plausible?
(b) Find the least squares estimates of the slope and inter-
cept in the simple linear regression model. Find an
estimate of ^2.
(c) Estimate the mean shear strength of a motor made from
propellant that is 20 weeks old.
(d) Obtain the fitted values that correspond to each ob-
served value yi. Plot versus yi, and comment on what
this plot would look like if the linear relationship betweenyˆiyˆiy 110 113 75 94x 35.5 43.0 40.5 33.0y 240 181 193 155 172x 1.6 9.4 15.5 20.0 22.0c 11 .qxd 5/20/02 1:15 PM Page 382 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH114 FIN L:Quark Files: