Question

0 pts) You are given the following estimated equation: In(wage) 0.1279+0.0904educ + 0.041 exper-0 (0.1059) (0.0075) (0.0052) (0.00012) R 0.3003 526 in which: log(wage) log of average hourly wage - educ is the number of years of schooling: - exper is the number of years of experience -exper'=experience"experience The plot of the residuals against the fitted values from the regression above, is provided below: .5 2.5 1.5 Fitted values a. With a 1% significance level, are the explanatory variables individually significant? (3 pts) b. Are the explanatory variables jointly significant (with a 1% significance level)? (1 pt) c. From observing the residual plot above, which assumption from the classical linear regression analysis appears not to be satisfied? (1pt) d. What are the possible consequences for the OLS estimators, resulting from the assumption found to be violated in question 'c"? (2pts) From an auxiliary regression of the squared residuals against the predicted values, and the squared predicted values, we obtained the following equation: residuals0.2946-0.3042 fittedvalues+0.1458 fittedvalues (0.2769) (0.3526) R2 0.0238 n 526 (0.1108) -326 (01108)

please be detailed in your response :) thank you!

Answer 1

to test for individual significance, we need to calculate the t-statistic for each variable and test it with the critical value from the t-table. degrees of freedom = n-k-1 where k is the number of variables, there dof= n-4 =522. It will be a t-test, hence significance level for t-test = 1-1%/2 = 0.995

t- statistic
intercept = 0.1279/0.1059 = 1.2078
educ = 0.0904/0.0075 = 12.0533
exp er = 0.041/0.0052 = 7.8846
exp er2 = 0.00071/0.00012 = 5.9167
critical value = 2.581, if t-statistic > critical value, then significant, therefore, educ, exp er and exp er2 aer significant

we conduct F test for joint significance, but need restricted and unrestricted sum of squares for this

residual errors are not normally distributed

the amount of error in the model is not consistent across the full range of your observed data. This means that the amount of predictive ability of the explanatory variables (i.e., as calculated in their beta weights) is not the same across the full range of the dependent variable. It represents a problem of heteroskedasticity, although the OLS estimator remains unbiased, the estimated SE is wrong.