Lab 7 HW

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Jonathan Allman ECON 3720: Introduction to Econometrics University of Virginia Ron Michener LABORATORY ASSIGNMENT 7 Please remember to include your do file with your submission. As before, if your submission does not include a do file you will be docked 5 points. This lab uses a small subset of data from one of the most famous regression analyses of all time, “Equality of Educational Opportunity,” by James S. Coleman, et al., 1966, commonly referred to as the Coleman Report. The report was commissioned to determine the extent and possible causes of educational inequality in the United States. Its sample included more than 150,000 pupils in schools across the U.S. The names and definitions of variables drawn from the Coleman Report for 20 schools in the northeast and middle Atlantic states appear below: Student_score i = the mean verbal achievement score for 6 th graders in school i; Salary i = staff salaries per pupil in school i; Pct_wc_dad i = the percent of 6 th graders in school i whose fathers have white-collar jobs; Ses i = a composite of different measures of the socio-economic status of the families of 6 th graders at school i. Higher values of Status correspond to higher levels of socio-economic status. Teacher_score i = teachers’ average verbal score at school i; Mom_ed i = average years of education of mothers of 6 th graders at school i. The underlying theory says that the more and better resources provided by the school, measured by staff salaries and teachers’ test scores, the better the school’s pupil performance will be; and the more affluent and better educated the pupils’ families, measured by fathers’ jobs, mothers’ schooling, and other variables incorporated in Status, the better the school’s pupil performance will be. STEP I : Compute the summary statistics for these variables and include that information in your report. F23 1 F23

STEP II : Fit a regression explaining student_score with pct_wc_dad and teacher_score, that is: . Include the result in your report. i) How would you interpret ? (Be precise!) For every one unit increase in “pct_wc_dad” we would expect on average an increase in “student_score” of approximately 16.5 . ii) Test the following hypothesis using : What is the correct p-value? Do you accept or reject the null hypothesis? What do you conclude? P value = (0.0000/2) = 0.0000 We reject the null hypotheses at the 5% significance level. We can conclude from this that the percentage of fathers with white collar jobs has a positive impact on test score. In this regression model. F23 2 F23

STEP III : Fit a regression explaining student_score with teacher_score and mom_ed; that is, . Include the result in your report. i) How would you interpret ?(Be precise!) For every one unit increase in “teachers_score” we can expect on average an increase 1.092213 in “student_score”. ii) Test the following hypothesis using : What is the correct p-value? Do you accept or reject the null hypothesis? What do you conclude? Mom-ed Pvalue= (0.130/2) = 0.065, We fail to reject the null hypothesis that beta2 is less than or equal to 0 at the 5% level. We can conclude from this, that a teacher’s average verbale score on average may have little to negative impact on a student’s test score. In this regression model. F23 3 F23

STEP IV : Fit a regression explaining student_score with teacher_score, mom_ed, and pct_wc_dad; that is, . Include the result in your report. Compare the coefficients of like variables with earlier regressions. Are they the same? Teachers verbale score had its highest coefficient of 1.3 when regressed with percentage of fathers with white collar jobs and its lowest when regressed with mothers’ average educational level of 1.09. Both coefficients of the variables “Pct_wc_dad” and “mom_ed” decreased when regressed together with “teachers_score”. The variables have changed with each regression. ii) Test the following hypothesis using : What is the correct p-value? Do you accept or reject the null hypothesis? What do you conclude? “Mom_ed” Pvalue (0.828/2) = .414, With a p value of .414 we fail to reject the null hypothesis that Beta 2 is less than or equal to zero. We can conclude from this that the level of a mothers education may have little to potentially a negative impact on a student’s test scores. In this regression model. iii) Test the following hypothesis using : What is the correct p-value? Do you accept or reject the null hypothesis? What do you conclude? “pct_wc_dad” Pvalue (0.118/2) = 0.59, With a p value of 0.59 we fail to reject the null hypothesis that Beta 3 is less than or equal to zero. We can conclude from this that the percentage of fathers with white collar jobs has little to potentially negative effects on a student’s test scores. In this regression model. F23 4 F23

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