Question

) Consider the following regression results based on 30 observations.

y = 238.33 – 0.95x1 + 7.13x2 + 4.76x3; SSE = 3,439

y = 209.56 – 1.03x1 + 5.24(x2 + x3); SSE = 3,559

a. Formulate the hypotheses to determine whether the influences of x2 and x3 differ in explaining y.

b. Calculate the value of the test statistic.

c. At the 5% significance level, find the critical value(s).

d. What is your conclusion to the test?

Answer 1

a.

The appropriate hypothesis for the jointly significance of x2 and x3 in explaining y are,

Null Hypothesis

Alternative Hypothesis

b.

Unrestricted Model :

y = 238.33 – 0.95x1 + 7.13x2 + 4.76x3; SSE = 3,439

Restricted Model :

y = 209.56 – 1.03x1 + 5.24(x2 + x3); SSE = 3,559

Test Statistic F = [(SSER - SSEU) / q] / [(SSEU / (n-k)]

where SSER , SSEU are SSE for restricted and unrestricted model.

q is number of restrictions in the null hypothesis.

n is number of observations

k is number of coefficients (including intercept) in unrestricted model.

Test Statistic F = [(3559 - 3439) / 1] / [3439 / (30-4)]

= 0.9072

c.

Numerator df = q = 1

Denominator df = n-k = 30-4 = 26

Critical value of F at 5% significance level and df = 1, 26 is 4.23

d.

Since the observed F (0.9072) is less than the critical value (4.23), we fail to reject the null hypothesis H0 and conclude that there is no strong evidence that the influences of x2 and x3 differ in explaining y.