The SAT has gone through many revisions over the years In 20

The SAT has gone through many revisions over the years. In 2005, a new writing section was introduced that includes a direct writing measure in the form of an essay. People argue that female students generally do worse on math tests but better on writing tests. Therefore, the new section may help reduce the usual male lead on the overall average SAT score (Washington Post, August 30, 2006). Consider the following portion of data on 20 students who took the SAT test last year. Information includes each student’s score on the writing and math sections of the exam. Also included are the student’s GPA and the values of a Gender dummy variable with 1 for females and 0 for males.

Estimate a linear regression model with math score as the response variable and GPA and the female dummy variable as the explanatory variables. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Compute the predicted math score for a male and female student with a GPA of 3.3. (Round your intermediate coefficient values and final answers to 2 decimal places.)

The SAT has gone through many revisions over the years. In 2005, a new writing section was introduced that includes a direct writing measure in the form of an essay. People argue that female students generally do worse on math tests but better on writing tests. Therefore, the new section may help reduce the usual male lead on the overall average SAT score (Washington Post, August 30, 2006). Consider the following portion of data on 20 students who took the SAT test last year. Information includes each student’s score on the writing and math sections of the exam. Also included are the student’s GPA and the values of a Gender dummy variable with 1 for females and 0 for males.

Solution

a-1.

Estimate a linear regression model with math score as the response variable and GPA and the female dummy variable as the explanatory variables. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

   = + GPA + Female.

Math =586.22 - 7.17 GPA+13.86 Female

a-2.

Compute the predicted math score for a male and female student with a GPA of 3.3. (Round your intermediate coefficient values and final answers to 2 decimal places.)

For male, Math =586.22-7.17*3.3+13.86*0 =562.559

For Female, Math =586.22-7.17*3.3+13.86*1 =576.419

Predicted values Answer

                           

  Male student 562.56

   

  Female student 576.42

  

Regression Analysis

R²

0.055

Adjusted R²

0.000

n

20

R

0.235

k

2

Std. Error

34.476

Dep. Var.

Math

ANOVA table

Source

SS

df

MS

F

p-value

Regression

1,179.3880

2  

589.6940

0.50

.6174

Residual

20,205.5620

17  

1,188.5625

Total

21,384.9500

19  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=17)

p-value

95% lower

95% upper

Intercept

586.2164

71.9410

8.149

2.84E-07

434.4342

737.9987

GPA

-7.1736

24.8637

-0.289

.7764

-59.6314

45.2842

Female

13.8607

15.6900

0.883

.3893

-19.2422

46.9636

a-1.	Estimate a linear regression model with math score as the response variable and GPA and the female dummy variable as the explanatory variables. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)