Question

Three equations for the course average of ADMS are estimated as follows. The first equation is for men, and the second equation is for women. The third equation combines men and women.

??=20.52+13.60?1+0.670?2 n = 406, R2 = 0.4025, SSR = 38,781.38
(3.72) (0.94) (0.150)
??=13.79+11.89?1+1.03?2 n = 408, R2 = 0.3666, SSR = 48,029.82
(4.11) (1.09) (0.18)
?=15.60+3.17?+12.82?1+0.838?2 n = 814, R2 = 0.3946, SSR = 87,128.96
(2.80) (0.73) (0.72) (0.116)

Where ym = course average for men, yw= course average for women, x1 = overall GPA, x2 = ACT score, m = 1 for men.

A. You are to conduct Chow test that the regression equations are same for men and women:
- 1. State the hypotheses.
- 2. Compute the test statistic
- 3. Based on the computed value above, draw your conclusion (show your educated guess without the table)

B. With the third equation, test if the dummy variable is significant.

C. With the two tests conducted above, do you find any inconsistency? If yes, how can you interpret this outcome?

Answer 1

ANSWER:

Given that,

a)

1)

The null hypothesis for the test is define as there is no break point such that,

2)

The test statistic is obtained using the formula,

Where,

RSS = Residual sum of square for combined model = 87,128.96

RSS₁ = Residual sum of square for model 1 = 38,781.38

RSS₂ = Residual sum of square for model 2 = 48,029.82

k = number of predictor = 3

n1 = 406

n2 = 408

3)

Critical value

The critical value for F statistic is obtained from F distribution table for degree of freedom for numerator = k = 3 and degree of freedom for denominator = n1+n2-2k = 406+408-6=808 and significance level = 0.05.

Since absolute value of F-statistic > F critical value, the null hypothesis is rejected.

b)

The significance of dummy variable is tested by calculating the t statistic as follow,

The critical t value is obtained from t distribution table for degree of freedom for numerator = n-k =814-3=811 and significance level = 0.05

Since t-statistic > t critical value, the null hypothesis is rejected. Hence there is significant effect of dummy variable on model.

c)

There is a added dummy variable (which is significant in model) in combined model while ignored in individual model which means the ignored variable can take any value and create inconsistency