Question

You are testing the null hypothesis that there is no relationship between two variables, X and Y. From your sample of n = 22, you determine that SSR = 80 and SSE = 20. Construct the ANOVA table, test for model significance at a 0.05 level of significance and state your conclusion, and calculate the coefficient of determination and interpret its meaning.

Answer 1

Since there are two are variables so degree of freedom of regression is

The degree of freedom of error is

Following is the completed ANOVA:

			ANOVA
	df	SS	MS	F	p-value
Regression	1	80	80/1=80	80/1=80	0
Error	20	20	20/20=1
Total	21	100

For p-value excel function used is : =FDIST(80,1,20)

Since p-value is less than 0.05 so model is significant.

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The R-square is

It shows that 80% variation in dependent variable is explained by independent variable.