More on constructing the ANOVA table. A multiple regression analysis of 73 cases

Question

More on constructing the ANOVA table. A multiple regression analysis of 73 cases was performed with 5 explanatory variables. Suppose that SSM=14.1 and SSE=100.5. Find the value of the F statistic for testing the null hypothesis that the coefficients of all of the explanatory variables are zero. What are the degrees of freedom for this statistic? Find bounds on the P-value using Table E. Show your work. What proportion of the variation in the response variable is explained by the explanatory variables?

Explanation / Answer

a) DFM = p-1 = 6-1 = 5
DFE = n-p = 73 - 6 = 67

MSM = SSM/DFM = 14.1/5 = 2.82
MSE = SSE/DFE = 100.5/67 = 1.5

F = MSM/MSE = 2.82/1.5 = 1.88

b) DFnumerator = 5, DFdenominator = 67

c) p = 0.1095

d) R2 = SSM/(SSM+SSE) = 14.1/(14.1+100.5) = 0.1230

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