Chapter 18 Homework
18.46 – perform using NCSS (except where formulas are required)
also, interpret the regression coefficient for ERA
Y   0  1 x1   2 x2   3 I   (first - order model with 3 predictors)
yˆ  .3571  .4005 x1  .0764 x 2  .0509 I
H 0 : 3  0
H 0 : 3  0
t*  8.606, tcrit  1.68
There is enough evidence to infer that a team that fires its manager within 12 months wins less
frequently than other teams. We can also say that for the times with the fired manager, estimated
win percentage is -.0509 percent less than those teams that did not fire their manager within the
last 12 months.
For each additional 1 point increase in ERA, we estimate a team’s win percentage increases by
.0764, holding the other variables constant or at a fixed level.
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18.48 – perform using NCSS (except where formulas are required)
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Y   0  1 x1   2 x 2   3 x 22   4 I 1   5 I 2   (second - order model with 5 predictors , no interaction)
yˆ  1003  .194 x1  256.6 x 2  17.76 x 22  1.07 I 1  1.16 I 2
where
x1 , temperature
x 2 , ph
I 1  1 if weather is mainly cloudy, 0 otherwise
I 2  1 if weather is sunny, 0 otherwise
partly sun ny is the base
H 0 : 1   2   3   4   5  0
H 1 : at least one  i is not 0
F *  77, Fcrit  F (.05,5,204)  2.258, pvalue  0
There is enough evidence to infer the model is valid.
Can we infer that higher temperatures deplete chlorine more quickly?
H 0 : 1  0
H 1 : 1  0
t*  6.78, tcrit  t (.05,204)  1.645, pvalue  0
There is enough evidence to infer that higher temperatures deplete chlorine more quickly.
Further, for each additional 1 degree increase in temperature, estimated chlorine depletion
increases by .194 percent.
There is enough evidence to infer that there is a quadratic relationship between chlorine depletion
and PH level. This is a test of significance for the beta3 coefficient.
H 0 : 3  0
H1 :  3  0
t*  18.07, tcrit  t (.05,204)  1.645, pvalue  0
What can we say about the weather as a factor in chlorine depletion?
H 0 :  i  0 (where i  4,5)
H1 : i  0
I 1 : t*  1.53, tcrit  t (.025,204)  1.96 and  1.96 , pvalue  .1282
There is not enough evidence to infer that chlorine depletion differs between mainly
cloudy days and partly sun ny days.
I 2 : t*  1.65, tcrit  t (.025,204)  1.96 and  1.96 , pvalue  .0997
There is not enough evidence to infer that chlorine depletion differs between sunny
days and partly sun ny days.
Weather is not a significa nt factor in chlorine depletion.
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