Question

A researcher is trying to decide whether or not to add another two variables to his model. He has estimated the following model from a sample of 27 observations. ?̂ = 25.2 + 5.5 ?1. For this estimated regression equation, SSE=520.

He has also estimated the model with an additional variables ?2 and ?3. The results are ?̂ = 16.3 + 2.3 ?1 + 12.1 ?2 − 5.8 ?3. For this estimated regression equation, SSE=100.

What advice would you give this researcher? Use a .05 level of significance

Answer #1

SSE_{1} = 520

SSE_{2} = 100

n = 27

m = 2

k = 4

H0: Coefficients of x2 and x3 are 0.

**Test Statistics Calculation:**

F =420*23/100*2

= 48.3

The F critical values for a two-tailed test, for a significance level of α=0.05, are

F_{L} =0.025 and F_{U} = 4.349

As F-value lies in the rejection region that means we reject the null hypothesis and hence coefficients of x2 and x3 are not 0

Thus the researcher should add x2 and x3 to his analysis.

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