With the data in the accompanying table, estimate GPA = 0 + 1 GRE + , where GRE
ID: 3437446 • Letter: W
Question
With the data in the accompanying table, estimate GPA = 0 + 1GRE + , where GRE is a student’s score on the math portion of the Graduate Record Examination score and GPA is the student’s grade point average in graduate school.
Construct a 90% confidence interval for the expected GPA for an individual who scored 710 on the math portion of the GRE. (Round your intermediate calculations to 4 decimal places, "t/2,df" value to 3 decimal places, and final answers to 2 decimal places.)
Construct a 90% prediction interval for the GPA for an individual who scored 710 on the math portion of the GRE. (Round your intermediate calculations to 4 decimal places,"t/2,df" value to 3 decimal places, and final answers to 2 decimal places.)
Explanation / Answer
With the data in the accompanying table, estimate GPA = 0 + 1GRE + , where GRE is a student’s score on the math portion of the Graduate Record Examination score and GPA is the student’s grade point average in graduate school.
GRE
700
720
650
750
680
730
740
780
GPA
3.0
3.5
3.2
3.7
3.1
3.9
3.3
3.5
a.
Construct a 90% confidence interval for the expected GPA for an individual who scored 710 on the math portion of the GRE. (Round your intermediate calculations to 4 decimal places, "t/2,df" value to 3 decimal places, and final answers to 2 decimal places.)
Confidence interval 3.17 to 3.55
b.
Construct a 90% prediction interval for the GPA for an individual who scored 710 on the math portion of the GRE. (Round your intermediate calculations to 4 decimal places,"t/2,df" value to 3 decimal places, and final answers to 2 decimal places.)
Prediction interval 2.81 to 3.92
Excel used for analysis
Regression Analysis
r²
0.345
n
8
r
0.587
k
1
Std. Error
0.268
Dep. Var.
GPA
ANOVA table
Source
SS
df
MS
F
p-value
Regression
0.2275
1
0.2275
3.16
.1260
Residual
0.4325
6
0.0721
Total
0.6600
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=6)
p-value
90% lower
90% upper
Intercept
0.2559
1.7725
0.144
.8899
-3.1884
3.7003
GRE
0.0044
0.0025
1.776
.1260
-0.0004
0.0092
Predicted values for: GPA
90% Confidence Interval
90% Prediction Interval
GRE
Predicted
lower
upper
lower
upper
Leverage
710
3.3617
3.1726
3.5509
2.8068
3.9167
0.131
GRE
700
720
650
750
680
730
740
780
GPA
3.0
3.5
3.2
3.7
3.1
3.9
3.3
3.5
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