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# Multiple Linear Regression

3.1 a. = −1.8 + .0036x2 + .194x7 − .0048x8
b. Regression is significant. c. All three are significant.
 Coefficient test statistic p-value β2 5.18 0.000 β7 2.20 0.038 β8 −3.77 0.001
d. R2 = 78.6% and R2Adj = 76.0%
e. F0 = (257.094 − 243.03)/2.911 = 4.84 which is significant at α = 0.05. The test statistic here is the square of the t-statistic in part c.
3.2 Correlation coefficient between yi and i is .887. So (.887)2 = .786 which is R2.
3.3 a. A 95% confidence interval on the slope parameter β7 is 7 ± 2.064(.08823) = (.012, .376)
b. A 95%. confidence interval on the mean number of games won by a team when x2 = 2300, x7 = 56.0 and x8 = 2100 is 3.4 a. = 17.9 + .048x7 − .00654x8 with F = 15.13 and p = 0.000 which is significant.
b. R2 = 54.8% and R2Adj = 51.5% which are much lower.
c. For β7, a 95% confidence interval is 0.484 ± 2.064(.1192) ...

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