Another extension of model 1 in Question 1 is Model 2, estimated for men and wom

Question

Another extension of model 1 in Question 1 is Model 2, estimated for men and women together. This model adds the interaction term age_woman = age * woman and the square of age (age_sq = age^2) to Model 1. The OLS estimation results are given below. Model 1 a. Discuss the estimated age pattern of housework for men and women using the estimates of model 2. b. Explain how you would construct a 95% prediction interval for housework of a retired man of age 50 with perfect health (you do not have to compute it). c. A Breusch-Pagan test for model 2 gives the following result: test statistic: F = 22.87; p-value = 0.0000. (i) What are the null hypothesis and the alternative hypothesis of this test? (ii) How the test statistic computed? What is the critical value? (iii) What is the conclusion of the test? What does this imply for the interpretation of the output of Model 2?

Explanation / Answer

The p-values for women and _cons are greater that 0.05 so these variables not significant to fit the model.

So we can eliminate them from the model.

All other variables have significant to fit the model because p-values of all are less than 0.05.

For the unit change in the variables is same as the mean change of dependent variable as their corresponding estimates value when other variables are constant.

b) By using standard deviation of residual and estimated value of housework for age = 50 , total sample size(n)

we can find prediction interval for predicted value y.

c) i) Null hypothesis H0: There is no heteroschedasticity (that is homoshedasticity) present that is variance of error term is constant.

alternative hypothesis H1:  H0: There is heteroschedasticity present that is variance of error term is not constant.

If the test statistic has a p-value below an appropriate threshold (e.g. p<0.05) then the null hypothesis of homoshedasticity) is rejected and heteroschedasticity assumed.

We have p-value = 0.0000 < 0.05 so the heteroschedasticity assumed in the data set.

Since the assumptions of constant variance are not satisfied so the estimated regression coefficient are not best to used population regression coefficients.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.