3. You gather data on 420 California school districts in 1999-2000 in order to d

Question

3. You gather data on 420 California school districts in 1999-2000 in order to determine whether or not class size is causally related to test scores in a district. You produce the following table: Results of Regressions of est Score on STR and Control Variables Dep. Variable: District Test Score STR 2.28 1.10 -1.00 -0.24 (0.52) (0.43) (0.27) (0,32) EL pot -0.65 -0.12 0.13 (0.031) (0.038) (0.032) Meal pot -0,55 0.55 (0.024) (0.023) Erpn Stud 0,0036 (0.00094) Constant 699 686*** 700 666 (0.4) (8.73) (5.57) Observations 420 120 420 R-squared 0.783 0.051 0.426 0.775 Robust standard errors in parentheses p

Explanation / Answer

Part-A

In column-1, 0=699 which is the average test score when STR=0

In column-3, , 0=686 which is the average test score when STR=EL_pct=Mean_PCT=0

Part-B

In column-1, coefficient of STR is -2.28 which means that corresponding to unit increase in student-teacher ratio there is on an average a decrease of 2.28 units in test scores, holding other predictors fixed

In column-3, coefficient of STR is -1.00 which means that corresponding to unit increase in student-teacher ratio there is on an average a decrease of 1.00 units in test scores, holding other predictors fixed

We expect a negative sign because as STR increases means there are more student than teacher and hence teachers has less time to take care of each student.

Part-C

In column-3, t-statistic for STR is t=-1.00/0.27=-3.704

We would retain it as it is significant even at 0.1 level of significance.

Part-D

From formula we have

F=[(0.783-0.426)/2]/[(1-0.783)/(420-4-1)]= 341.37

As calculated F>3.00 we reject the null hypothesis and conclude that Meal_pct and Expn_stu are jointly significant

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