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- A researcher is studying the effect of smoking on birth weight. Using data on average cigarettes smoked per day (cigs), mother’s level of education (meduc), father’s level of education (feduc), and logarithm of family income (l.income), the researcher estimates 3 models. Table (1) shows the OLS estimates for each model, with standard errors in parentheses underneath each coefficient. The dependent variable in all the models is birth weight.
Table (1)
| Model 1 | Model 2 | Model 3 | |
| Dependent variable | Birth weight (ounces) | Birth weight (ounces) | Birth weight (ounces) |
| Independent variables | |||
| Average number of cigarettes smoked per day during pregnancy by the mother (cigs) | -0.47
(0.09) |
-0.39
(0.09) |
-0.35
(0.07) |
| Natural logarithm of annual family income (l.income) | 1.84
(0.59) |
||
| Mother’s completed years of education (meduc) | -0.37
(0.20) |
||
| Father’s completed years of education (feduc) | 0.41
(0.32) |
||
| Intercept | 116.974
(1.049) |
114.032
(1.946) |
115.675
(2.981) |
| N | 1388 | 1388 | 1388 |
| R2 | 0.029 | 0.030 | 0.045 |
a.Interpret the R-squared of the regression in model 1.[5 marks]
b.Test at the 5% level whether smoking has a statistically negative effect on birth weights, using the estimate in model 1. [6 marks]
c.Carefully interpret the coefficient of incomein model 2. [5 marks]
d.The two variables that measure the effect of parental education in model 3 above are not statistically significant. Would you keep these two variables in the model? Carefully explain your answer and provide any necessary evidence to support your answer. [8 marks]
e.Explain what is multicollinearity and suggest a method to measure it in model 3. [6 marks]
2.The variable descriptions and Stata outputs from the simple and multiple linear regression are available in the exam handout file. Use this file to answer the following questions.
a.Firstly, report the results from the regression of wageon educ in the form of a fitted line, with the standard error of coefficients presented in parentheses underneath the corresponding coefficients. Round the numbers to two decimal places. [4 marks]
b.Is the coefficient of educstatistically significant? [3 marks]
c.Now consider the multiple linear regression that includes KWW as one of the explanatory variables. Between this regression and the simple linear regression in part (a), which model is more likely to measure the ceteris paribus effect of education on wages? Explain and when possible use evidence to support your answer. [8 marks]
d.What happened to the standard error of educafter adding KWW to the model? Discuss. [10 marks]
e.Do you agree or disagree with the following statement? “If the log of the dependent variable appears in the regression, changing the unit of measurement of any independent variable affects both the slope and intercept coefficients”. Discuss [5 marks]
3.A researcher is commissioned by a policy maker to conduct an empirical investigation. The researcher needs to collect data and hence asks the policy maker for a grant. After the grant application is approved the researcher demands for more financial support to collect more data and increase its sample size. The researcher claims that the advantage of a bigger sample size is removing the bias from estimation.
a.Explain omitted variable in linear regressions. [5 marks]
b.Based on what you learnt in this module, do you agree or disagree with the researcher’s claim that “bigger sample size removes the omitted variable bias”. Discuss. [10 marks]
Section B
Attempt one question from this section for maximum of 25 marks
SECTION 3 – Answer one question from this section
4.A researcher is interested to know whether class attendance affects the outcome of a final exam among college students. The researcher obtains the following OLS estimates:
Final= 32 + 0.008 attendance – 8.98 priGPA + 2.3 (1)
(2.9) (0.033) (2.29) (0.42)
n = 680; = 0.169
Where final is the score of the student in the final exam, attendance is the percentage of classes the student attended, and priGPA is the prior college grade point average. For example, for a student in the fourth semester, priGPA measures his/her GPA of the first three semesters. Standard errors are in parentheses.
a.In one or two sentences explain what the increasing marginal returns mean in this example. [4 marks]
b.Is there evidence for increasing marginal returns to priGPA? [4 marks]
c.Sketch a graph illustrating the relationship between final and priGPA, and calculate at what age priGPA is predicted to decline.[5 marks]
d.And finally, the researcher wants to test whether his estimates suffer from heteroscedasticity. Use the auxiliary regression below to test for the presence of heteroscedasticity. is the square of the estimated residuals from model (4) above. and are the predicted values of final score and the squared predicted values of final score, respectively.[10 marks]