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Please show your work step-by-step. 45. The following regression equation was obtained using the fie independent variables. Given that alpha = 0. 05 45. The following regression equation was obtained using the fie independent variables. Given that alpha = 0. 05 a) What percent of the variation is explained by the regression equation? b) What is the standard error of regression? c)What is the critical value of the F-statistic? d) What sample size is used in the print out? e)What is the variance of the slope coefficient of income? f) Conduct a global test of hypothesis to determine if any of the regression coefficients are not zero. g) Conduct a test of hypothesis on each of the independent variables. Would you consider eliminating outlets and bosses?

Solution

(a) Since r-square is 99.4% so variation explained by the regression equation is 99.4%.

(b) Standard error of regression is 1.507.

(c) Degree of freedom of F -test is df1=5, df2=4 so for alpha =0.05 critical value of F is 6.526.

(d) Sample size is n=4+5+1=10.

(e) estimated standard deviation of the income is 0.04385. So variance will be 0.04385*0.04385=0.0019.

(f) From ANOVA table F is 140.36 and P-value is 0.000. Since P-value is less than 0.05 so we reject the null hypothesis. On the basis of sample evidence one can conclude that there is one or more regression coefficient are not equal to 0.

(g) Since P-value of the cars and income is less than 0.05 so these are significant for the model.