We analyse a data set that consists of test scores and class sizes of 420 1'v'ictorian 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 studentteacher ratio [5TH], that isl the number of students in the district divided bv the number of teachers. We obtain following 0L5 regression result for model {1}, the standard errors are presented in parentheses: TsstScors = 698.9 2.28 STE {10.4} {13.52} n = 42o, R2 = [1.051. {a} Interpret the intercept and slope coefficients. {2 marks] {b} What is the predicted test score for a district with a studentteacher ratio of 13? {2 marks] {4:} Test the null hvpothesis that the studentteacher ratio has a significantlyf negative effect on the test score at 5% level of significance. Specifv all detailed steps of the test. {4 marks] {d} One concern of the simple regression model above is that the studentteacher ratio might be picking up the effect of having manv students for whom English is a second language, i.e. English learners. We add the variable PctEl. representing the percentage of English learners in the school district and obtain the following OILS regression result for model [I]: 4 Test Score = 686.0 - 1.10 STR - 0.65 PctEL (8.7) (0.43) (0.031) n = 420, R3 = 0.415. Compare the results of models (1) and (2), which model is better? Explain why. (4 marks)