Question

Can you please answer the 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 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.

SCORE	STR	TSAL	INC	SGL
227.00	19.00	44.01	48.89	4.70
230.67	17.90	40.17	43.91	4.60
⋮	⋮	⋮	⋮	⋮
230.67	19.20	44.79	47.64	5.10

SOURCE: Massachusetts Department of Education and the Census of Population and Housing.

Click here for the Excel Data File

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

Explanatory variable	Effect on score
STR
TSAL
INC
SGL

b-1. Estimate the sample regression equation. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

ScoreˆScore^ =  +  STR +    TSAL +    INC +  SGL

b-2. Are the signs of the slope coefficients as expected?

Coefficient	IS THE SIGN EXPECTED ?
SGL
INC
TSAL
STR

c. What is the predicted score if STR = 18, TSAL = 50, INC = 60, SGL = 5? (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

ScoreˆScore^

d. What is the predicted score if everything else is the same as above except INC = 80? (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

ScoreˆScore^

Answer 1

From the given data,

a) explanatory variable Effect on score

STR Negative effect

TSAL Positive effect

INC positive effect

SGL Negative effect.

b)

c)

d)