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Use the data in MEAPOO to answer this question.(i) Estimate the model Estimate the model$m a t h 4=\beta_{0}+\beta_{2} l e x p p p+\beta_{2} l e n r o l l+\beta_{3} \operatorname{lunch}+u$by OLS, and report the results in the usual form. Is each explanatory variable statistically significant at the 5$\%$ level?(ii) Obtain the fitted values from the regression in part (i). What is the range of fitted values? How does it compare with the range of the actual data on $\operatorname{math} 4$ ?(iii) Obtain the residuals from the regression in part (i). What is the building code of the school that has the largest (positive) residual? Provide an interpretation of this residual.(iv) Add quadratics of all explanatory variables to the equation, and test them for joint significance.Would you leave them in the model?(v) Returning to the model in part (i), divide the dependent variable and each explanatory variable by its sample standard deviation, and rerun the regression. (Include an intercept unless you also first subtract the mean from each variable.) In terms of standard deviation units, which explanatory variable has the largest effect on the math pass rate?

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Chapter 6

Multiple Regression Analysis: Further Issues

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Arfiani N.

March 21, 2022

Use the data in MEAP00.RAW to answer this question. (i) Estimate the model math4 5 b0 1 b2lexppp 1 b2lenroll 1 b3lunch 1 u by OLS, and report the results in the usual form. Is each explanatory variable statistically significant at the 5% level? (ii) Obtai

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This is the regression result for Part one. We have the dependent. Variable is the number of the percent of student who passed the fourth grade math test, and we have the lock of expenditure per student, lock of enrollment and whether the student can receive free or reduced lunch. Reduced price lunch. So I have the estimates in blue and the standard arrows in green and in bracket. The R square of the regression is 0.373 and we have almost 1700 observations in the regression. As you may see from your statistical package, we have thes two variable lock of enrollment and lunch are individually significant at the 5% level. Okay, but for lock of expenditure per student, these variable has a T statistic of 1.68 And so it is not significant against a two sided alternative that is part one. And for part two, we will get a fitted value of math. Four. From the regression, we see that the range of fitted value runs from 42.41 to 92 point 67. This is this range is much narrower than the range of actual math pass rates in the sample, which is from 0 to 100. In Part three, we will do a residual examination. We find that the largest residual is about 51.42 but this residual belongs to you, building code 11 41. But the residual is the difference between the actual past rate and our best prediction of the past rate. If we think that per student spending enrollment and the lunch indicator as sufficient controls, then the residual can be interpreted as a value added for the school. So for school 11 41 it's past rate is over 51 points higher than we would expect based on its spending size and student poverty. Part four. We will do another regression. We went at the quadratic six. Let's see the quarter tricks off all explanatory variables, and we will test for joint significance of these quadratic six. So we will do an F test and are not. Hypothesis is all quadratic. Six, um are not meaningful. We will get an F statistic with two degrees of freedom. The first one is three, and the second one is 1600 85 the F statistic is about 0.52 and the P value is 0.67 So we are unable to reject the null hypothesis, which means the Quad atrix are jointly very insignificant. And so we should drop them from the model for the last part. You win, do another regression. What? You in return to the model in part one and divide the dependent variables and each explanatory variables by ease by its central division. Then you re run the regression. This is a very common technique when you have, um, incomparable variables. Okay, so we don't care about the estimation of the intercept. We only care about the slopes we have there. Oh, beta coefficients. For lot of expenditure per student of 0.53 four. Lock of enrollment as minus 0.115 and four lunch. The beta coefficient is minus 0.613 So instead, activation units lunch has by far the largest effect. The spending variable has the smallest effect

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