With the data in the accompanying table estimate GPA 0 1GR

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.)

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

Solution

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