It is assumed that standardized test scores should be correlated with students c
ID: 3159707 • Letter: I
Question
It is assumed that standardized test scores should be correlated with students classroom performance. One would expect that students who consistently perform well in the classroom (tests, quizzes, etc.) would also perform well on a standardized test (0 - 100 with 100 indicating high achievement). A teacher decides to examine this hypothesis. At the end of the academic year, she collects the following data for her (small) class:
(a) Estimate the expected GPA of a student who scored a 75 on the standardized test.
(b) Determine a 99% confidence interval for the expected value of a student who scored a 70 on the standardized test.
Explanation / Answer
Regression Analysis
r²
0.950
n
5
r
0.975
k
1
Std. Error
0.187
Dep. Var.
Overall GPA
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1.9832
1
1.9832
56.77
.0048
Residual
0.1048
3
0.0349
Total
2.0880
4
Regression output
confidence interval
variables
coefficients
std. error
t (df=3)
p-value
99% lower
99% upper
Intercept
-0.2822
0.4201
-0.672
.5499
-2.7360
2.1717
Test score
0.0391
0.0052
7.535
.0048
0.0088
0.0694
Predicted values for: Overall GPA
99% Confidence Intervals
99% Prediction Intervals
Test score
Predicted
lower
upper
lower
upper
Leverage
75
2.6481
2.1420
3.1542
1.4448
3.8514
0.215
70
2.4527
1.8876
3.0179
1.2234
3.6820
0.268
The estimated regression line
Overall GPA = -0.2822+0.0391*test score
Estimated Overall GPA = -0.2822+0.0391*75
=2.6503
(b) Determine a 99% confidence interval for the expected value of a student who scored a 70 on the standardized test.
99% confidence interval =(1.8876, 3.0179).
Regression Analysis
r²
0.950
n
5
r
0.975
k
1
Std. Error
0.187
Dep. Var.
Overall GPA
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1.9832
1
1.9832
56.77
.0048
Residual
0.1048
3
0.0349
Total
2.0880
4
Regression output
confidence interval
variables
coefficients
std. error
t (df=3)
p-value
99% lower
99% upper
Intercept
-0.2822
0.4201
-0.672
.5499
-2.7360
2.1717
Test score
0.0391
0.0052
7.535
.0048
0.0088
0.0694
Predicted values for: Overall GPA
99% Confidence Intervals
99% Prediction Intervals
Test score
Predicted
lower
upper
lower
upper
Leverage
75
2.6481
2.1420
3.1542
1.4448
3.8514
0.215
70
2.4527
1.8876
3.0179
1.2234
3.6820
0.268
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.