Education reform is one of the most hotly debated subjects on both state and national policymakers’ 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 to 10th graders. Four predictor variables are used: (1) STR is the student-to-teacher ratio in %, (2) TSAL is the average teacher’s salary in $1,000s, (3) INC is the median household income in $1,000s, and (4) SGL is the percentage of single-parent households. A portion of the data is shown in the accompanying table. Required:
a. For each predictor variable, discuss whether it is likely to have a positive or negative influence on Score.
b-1. Estimate the sample regression equation. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
b-2. Are the signs of the slope coefficients as expected?
c. What is the predicted score if STR = 18, TSAL = 50, INC = 60, SGL = 5? (Do not round intermediate calculations. Round final answer to 2 decimal places.)
d. What is the predicted score if everything else is the same as above except INC = 80? (Do not round intermediate calculations. Round final answer to 2 decimal places.)