In a regression analysis involving 30 observations, the following estimated regr

Question

In a regression analysis involving 30 observations, the following estimated regression equation was obtained. y ˆ = 17.6 + 3.8x1 - 2.3x2 + 7.6x3 + 2.7x4 For this estimated regression equation SST = 1805 and SSR = 1,772. Compute the following (to 1 decimal, if necessary). SSE 33 MSR 335.61 MSE What is the value of the F test statistic (to 2 decimals)? What is the p-value? Using = .05, what is your conclusion? Suppose x1 and x4 are dropped from the model and the following estimated regression equation is obtained. y ˆ = 11.1 - 3.6x2 + 8.1x3 For this model SST = 1805 and SSR = 1705. Compute SSE for this model. Use an F test and = .05 to determine whether x1 and x4 contribute significantly to the model. What is the value of the F test statistic (to 2 decimals)? What is the p-value? What is your conclusion about the two variables x1 and x4?

Explanation / Answer

The F test statistic, F=MSR/MSE=335.61/1.27=264.26

MSE=SSE/n-k=33/30-4=33/26=1.27

p value is: 0.0000

The p value is less than alpha=0.05, reject H0 to cocnclude that at least on epopulation mean is different.

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