We analyse a data set that consists of test scores and class sizes of 420 Victorian school districts in 2020 that serve kindergarten through eighth grade. The test score is the district-wide average of reading and math scores for sixth graders. Class size is measured by the student-teacher ratio (STR), that is, the number of students in the district divided by the number of teachers.

We obtain following OLS regression result formodel (1), the standard

errors are presented in parentheses:

Test score HAT= 698.92.28STR

(10.4) (0.52)

n = 420, R2= 0.051.

1. (a) What is the predicted test score for a district with a student-teacher ratio of 18?
2. Test the null hypothesis that the student-teacher ratio has a significantly negative effect on the test score at 5% level of significance. Specify all detailed steps of the test.
3. One concern of the simple regression model above is that the student-teacher ratio might be picking up the effect of having many students for whom English is a second language, i.e. English learners. We add the variablePctELrepresenting the percentage of English learners in the school district and obtain the following OLS regression result formodel (2):

Test score HAT= 686.01.10STR 0.65PctEL

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(8.7) (0.43) (0.031)

n = 420, R2= 0.415.

Compare the results of models (1) and (2), which model is better? Explain why.

Please can someone help me?