uppose there is a study of college graduation rates across a series of high schools in a region. The study shows that increased spending in the high school, per capita, increases graduation rates. From the initial information presented in the study you know the following:
There are 95 high schools that data were obtained from in the region
The correlation between per capita spending in high school and college graduation rate is .35.
A regression of Y = a + bX, where Y is the college graduation rate and X is the per capita spending on high school education gives parameter estimates of .2145 for a and .0473 for b. The standard errors of these are .1055 and .0133 respectively.
Discuss these results. Include interpretation of what these results mean, the statistical properties of the estimation and estimates, what problems are likely to exist in these data, and what next steps are appropriate for gaining better understanding of the underlying issue. What changes should be made to this study? Do you feel that results would change if these changes were made?Suppose a second study, using the same data as in the previous discussion thread, is completed and the results presented.
The estimation is now Y = a + b1x1 + b2x2 where Y is still college graduation rate, x1 is still per student spending on high school education, and x2 is the percent of students' households with a college degree (parent or older sibling).
The study reports parameter estimates of -.009, .0433, and .4657 with standard errors of .0722, .0088, and .0419 respectively.
The study also reports an adj R2 of .6244 and a model F of 76.47.Suppose yet another study is performed on the graduation rate data. A new variable has been obtained which is the average number of hours parents state that their children work on schoolwork at home per week. The regression that is now run is of the form:
CGR = b0 + b1 * hs$/cap + b2 * deg in house + b3 * hours/week + e
and the results are
b0 = XXXXXXXXXX)
b1 = XXXXXXXXXX)
b2 = XXXXXXXXXX)
b3 = XXXXXXXXXX)
The model F for this estimation is 706.2 and the R-squared is .9588
Compare these results to the original and second model and describe the changes. Be sure (as a group) to include information on goodness of fit, changes in significance in the parameters as variables are added, influences on the graduation rate, and other relevant interpretations.
What doe these changes tell us about the correlations found in the earlier models and how much of these changes do you anticipate will survive further changes in the study? Do any of the results make sense? Are any counter-intuitive? Discuss the results, primarily from an econometrics perspective, but also from what these studies (as an evolving group) tell us.Why are these results so different from the earlier results? What are the econometric reasons in addition to the "economic" reasons.