Question

Source	DF	SS	MS	F
Model	4	70
Error
Total	33	524

What is DFE?

What percentage of the variation in the response variable is explained by the explanatory variables? (report as %)

What is the range for the p-value for the above?

Answer 1

Solution:

Given:

Source	DF	SS	MS	F
Model	4	70
Error
Total	33	524

Part a) What is DFE?

DFE = Degrees of Freedom for Error

DFE = DF Total - DF Model

DFE = 33 - 4

DFE = 29

Part b) What percentage of the variation in the response variable is explained by the explanatory variables? (report as %)

Thus 13.36% of the variation in the response variable is explained by the explanatory variables.

Part c) What is the range for the p-value for the above?

First complete ANOVA table to get F value.

SSE = SST - SSR

SSE = 524 - 70

SSE = 454

MSR = SSR / DFR

MSR = 70 / 4

MSR = 17.5

MSE = SSE / DFE

MSE = 454 / 29

MSE = 15.66

Thus

F = MSR / MSE

F = 17.5 / 15.66

F = 1.12

Source	DF	SS	MS	F
Model	4	70	17.5	1.12
Error	29	454	15.66
Total	33	524

Thus look in F table for df numerator = DFR = 4 and df denominator = DFE = 29 and find interval in which F = 1.12 fall then find corresponding right tailed area interval.

F = 1.12 < 2.15

Right tail area for F = 2.15 is 0.100

that means Right tail area for F = 1.12 > 0.100

Thus p-value > 0.100