The SAT has gone through many revisions over the years. In 2005, a new writing s
ID: 3437024 • Letter: T
Question
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.
Explanation / Answer
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.)
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