For a multiple linear regression

a) Provide summary measures (at least two) of the fit of the model. Based on the summary measures, does the model provide a good fit for the data? Explain.

b) How to use the residuals against the fitted values plot to check whether the usual model conditions are met.

c) When we are doing multiple linear regression, we often discard some data. Identify those missing values and explain what they are and why they were recorded as missing.

d) Test the marginal contribution of X1, assuming that the other variables in the model

remain constant. Use a 1% significance level. So II need use H0: beta1 = 0 ?

SUMMARY OUTPUT Regression Statistics Multiple R 0.951823737 R Square 0.905968426 Adjusted R Square 0.897420101 Standard Error 2.325540952 Observations 97 ANOVA df SS MS F Significance F Regression 8 4585.323823 573.1654778 105.981983 8.09669E-42 Residual 88 475.9163835 5.408140721 Total 96 5061.240206 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept 22.08295366 3.164654851 6.977997507 5.35494E-10 15.79386715 28.37204017 13.7508667 30.41504063 Number -0.000432408 0.000641955 -0.673579553 0.502343987 -0.001708159 0.000843343 -0.002122584 0.001257769 Nearest 0.266939825 0.277004314 0.963666672 0.337853757 -0.28354804 0.81742769 -0.462373209 0.996252859 Enrollment 0.073087875 0.057385802 1.273622964 0.206150865 -0.040954348 0.187130098 -0.078000795 0.224176546 Income 0.037785571 0.06338499 0.596128064 0.552619994 -0.088178776 0.163749919 -0.129098108 0.204669251 Distance 0.021311633 0.076858142 0.277285298 0.782211381 -0.131427773 0.174051039 -0.181044943 0.223668209 Quality 6.488623234 0.435243497 14.90803029 8.33618E-26 5.623668244 7.353578223 5.342688894 7.634557573 High Speed Internet 2.686949717 0.616119599 4.361084638 3.50353E-05 1.462541483 3.911357951 1.064794279 4.309105155 Gym 0.716798133 0.568794255 1.260206353 0.210926482 -0.413560924 1.847157191 -0.780756392 2.214352659