# Question

Education reform is one of the most hotly debated subjects on both state and national policy makers’ list of socioeconomic topics. Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders.

Four explanatory variables are used:

(1) STR is the student-to-teacher ratio,

(2) TSAL is the average teacher’s salary,

(3) INC is the median household income, and

(4) SGL is the percentage of single family households. A portion of the data is shown in the accompanying table; the entire data set, labeled MCAS, can be found on the text website.

a. For each explanatory variable, discuss whether it is likely to have a positive or negative causal effect on Score.

b. Find the sample regression equation. Are the signs of the slope coefficients as expected?

c. What is the predicted score if STR = 18, TSAL = 50, INC = 60, SGL = 5?

d. What is the predicted score if everything else is the same as in part c except INC =80?

Four explanatory variables are used:

(1) STR is the student-to-teacher ratio,

(2) TSAL is the average teacher’s salary,

(3) INC is the median household income, and

(4) SGL is the percentage of single family households. A portion of the data is shown in the accompanying table; the entire data set, labeled MCAS, can be found on the text website.

a. For each explanatory variable, discuss whether it is likely to have a positive or negative causal effect on Score.

b. Find the sample regression equation. Are the signs of the slope coefficients as expected?

c. What is the predicted score if STR = 18, TSAL = 50, INC = 60, SGL = 5?

d. What is the predicted score if everything else is the same as in part c except INC =80?

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