What percent of the variation is explained by the regression

What percent of the variation is explained by the regression equation? What is the standard error of regression? What is the critical value of the F-statistic? What sample size is used in the print out? What is the variance of the slope coefficient of income? Conduct a global test of hypothesis to determine if any of the regression coefficients are not zero. Conduct a test of hypothesis on each of the independent variables. Would you consider eliminating outlets and bosses?

Solution

a. R² = 99.4%

So, Percentage of variation explained = 99.4%

b. Standard error of regression = S = 1.507

c. Critical value of F statistic: F_5,4,0.05 = 6.26

d. Sample size = Total df + 1 = 9+1 = 10

As total df = n-1

e. Variance of slope coefficient of income = SE coeff of income ² = 0.04385² = 0.0019228

f. To test if regression coefficients are zero or not,

Test statistic = F stat = 140.36

P - Value = 0.000

As p value < 0.05, we reject the null hypothesis that all regression coefficients are zero. At least one regression coeff. is significantly different from zero.

g. P- value of outlet and bosses are > 0.10, so they are not statistically significantly different from zero, so they may be dropped while other variables are significant as p value < 0.10