380 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION11-1. An article in Concrete Research (“Near Surface
Characteristics of Concrete: Intrinsic Permeability,” Vol. 41,
1989), presented data on compressive strength xand intrinsic
permeability yof various concrete mixes and cures. Summary
quantities are n14, gyi 572, g 23,530, gxi 43,
157.42, and gxiyi 1697.80. Assume that the two vari-
ables are related according to the simple linear regression model.
(a) Calculate the least squares estimates of the slope and intercept.
(b) Use the equation of the fitted line to predict what perme-
ability would be observed when the compressive strength
is x4.3.
(c) Give a point estimate of the mean permeability when
compressive strength is x3.7.
(d) Suppose that the observed value of permeability at x3.7 is
y46.1. Calculate the value of the corresponding residual.
11-2. Regression methods were used to analyze the data
from a study investigating the relationship between roadway
surface temperature (x) and pavement deflection (y). Summary
quantities were n20, gyi 12.75, 8.86, gxi
1478, gxi^2 143,215.8, and gxiyi 1083.67.gyi^2gxi^2y^2 i(a) Calculate the least squares estimates of the slope and in-
tercept. Graph the regression line.
(b) Use the equation of the fitted line to predict what pave-
ment deflection would be observed when the surface
temperature is 85 F.
(c) What is the mean pavement deflection when the surface
temperature is 90 F?
(d) What change in mean pavement deflection would be ex-
pected for a 1 F change in surface temperature?
11-3. Consider the regression model developed in Exercise
11-2.
(a) Suppose that temperature is measured in C rather than F.
Write the new regression model that results.
(b) What change in expected pavement deflection is associ-
ated with a 1 C change in surface temperature?
11-4. Montgomery, Peck, and Vining (2001) present data
concerning the performance of the 28 National Football
League teams in 1976. It is suspected that the number of games
won (y) is related to the number of yards gained rushing by an
opponent (x). The data are shown in the following table.Yards
Games Rushing by
Teams Won (y) Opponent (x)
Washington 10 2205
Minnesota 11 2096
New England 11 1847
Oakland 13 1903
Pittsburgh 10 1457
Baltimore 11 1848
Los Angeles 10 1564
Dallas 11 1821
Atlanta 4 2577
Buffalo 2 2476
Chicago 7 1984
Cincinnati 10 1917
Cleveland 9 1761
Denver 9 1709Yards
Games Rushing by
Teams Won (y) Opponent (x)
Detroit 6 1901
Green Bay 5 2288
Houston 5 2072
Kansas City 5 2861
Miami 6 2411
New Orleans 4 2289
New York Giants 3 2203
New York Jets 3 2592
Philadelphia 4 2053
St. Louis 10 1979
San Diego 6 2048
San Francisco 8 1786
Seattle 2 2876
Tampa Bay 0 2560SSESST ˆ 1 Sxy (11-14)where is the total sum of squares of theresponse
variable y. The error sum of squares and the estimate of ^2 for the oxygen purity data,
are highlighted in the Minitab output in Table 11-2.EXERCISES FOR SECTION 11-2ˆ^2 1.18,SSTg
n
i 11 yˆi^ y^2(^2) gn
i 1 yi
(^2) ny 2
The resulting computing formula is
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