. Does school size affect student test scores? Using data from 408 high schools
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Question
. Does school size affect student test scores? Using data from 408 high schools from Michigan the following regression is estimated (standard errors are in parenthesis) Model 1 (6.113) (0.00010) (0.040) (0.00022) N- 408 adj-R2 0.054 where score, the average score (0-100) of 10th graders in a math test in high school i. avgcomp,is the average salary (in dollars) of teachers in high school i. staff the number of teachers (per thousand students) in high school i. enrollment,-the number of students in high school a) By how much are scores expected to change when avgcomp increase? (This is the same as asking what is the real-world interpretation of the coefficient of avgcomp? The same question as in the previous homework) Now consider that a second model is estimated changing the functional form of the independent variables by taking natural logs. The following regression equation is estimatedExplanation / Answer
a) the expected sign on avgcomp is positive because when the salary of the teachers increase , they become more incentivised to improve their teaching and hence there will be an improvement in test scores.
b) i) The expected sign of the coefficient is positive because as more number of teachers leads to more personalised attention and hence improvement in student learning leading to better scores
ii) Null hypotheis : B2 = 0
Alternate hypothesis : B2 =/( is not equal to) 0
c) i) The expected sign of enrollment would be negative as larger schools induce lower student outcomes as per the senator
ii) Null Hypothesis : B3 = 0
Alternate Hypothesi : B3 =/(is not equal to ) 0
d) i) The coefficient on staff is 0.048 which implies that with an increase in staff by one teacher, the student score would increase by 0.048 i.e the contribution of one additional teacher to the student outcome is 0.048
ii) The p value of the coefficient is 0.040 and hence the coefficient is statistically significant at 5 % level of significance and the null hypothesis is not rejected
iii) Yes it is true that teachers per student improve performance as students get more attention and supervision
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