The following data are the monthly salaries y and the grade point averages x for
ID: 3258047 • Letter: T
Question
The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration.
The estimated regression equation for these data is = -350 + 1,250x and MSE =236,875.
a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal).
$
b. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA (to 2 decimals).
$ ( , )
c. Develop a 95% prediction interval for Ryan Dailey, a student with a GPA of 3.0 (to 2 decimals).
$ ( , )
Explanation / Answer
Answer:
The estimated regression equation for these data is y = -350 + 1,250x and MSE =236,875.
a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal).
$3400.0
b. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA (to 2 decimals).
$ (2767.20 ,4032.80 )
c. Develop a 95% prediction interval for Ryan Dailey, a student with a GPA of 3.0 (to 2 decimals).
$ ( 1907.88 , 4892.12 )
Regression Analysis
r²
0.556
n
6
r
0.746
k
1
Std. Error
486.698
Dep. Var.
Monthly Salary ($)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,187,500.0000
1
1,187,500.0000
5.01
.0887
Residual
947,500.0000
4
236,875.0000
Total
2,135,000.0000
5
Regression output
confidence interval
variables
coefficients
std. error
t (df=4)
p-value
95% lower
95% upper
Intercept
-350.0000
1,797.5144
-0.195
.8551
-5,340.7001
4,640.7001
GPA
1,250.0000
558.2810
2.239
.0887
-300.0364
2,800.0364
Predicted values for: Monthly Salary ($)
95% Confidence Interval
95% Prediction Interval
GPA
Predicted
lower
upper
lower
upper
Leverage
3
3,400.000
2,767.200
4,032.800
1,907.880
4,892.120
0.219
Regression Analysis
r²
0.556
n
6
r
0.746
k
1
Std. Error
486.698
Dep. Var.
Monthly Salary ($)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,187,500.0000
1
1,187,500.0000
5.01
.0887
Residual
947,500.0000
4
236,875.0000
Total
2,135,000.0000
5
Regression output
confidence interval
variables
coefficients
std. error
t (df=4)
p-value
95% lower
95% upper
Intercept
-350.0000
1,797.5144
-0.195
.8551
-5,340.7001
4,640.7001
GPA
1,250.0000
558.2810
2.239
.0887
-300.0364
2,800.0364
Predicted values for: Monthly Salary ($)
95% Confidence Interval
95% Prediction Interval
GPA
Predicted
lower
upper
lower
upper
Leverage
3
3,400.000
2,767.200
4,032.800
1,907.880
4,892.120
0.219
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