The median grant and the average indebtedness (in dollars) at graduation for a r
ID: 3126159 • Letter: T
Question
The median grant and the average indebtedness (in dollars) at graduation for a random sample of students at public graduate schools of law are shown here. Is there a relationship between the variables? What is the equation of the regression line (if applicable)? Find y` when X = 4500 Median Grants.
Median Grant, X
1500
5500
1040
3508
3823
6000
1400
7000
Avg. Indebt, Y
39759
46790
44650
40000
51249
46500
42332
60000
Median Grant, X
1500
5500
1040
3508
3823
6000
1400
7000
Avg. Indebt, Y
39759
46790
44650
40000
51249
46500
42332
60000
Explanation / Answer
The median grant and the average indebtedness (in dollars) at graduation for a random sample of students at public graduate schools of law are shown here.
Is there a relationship between the variables?
Calculated F=6.15, P=0.0478 which is < 0.05 levlel.
The regression is significant.
There is significant relationship between the variables median grant and the average indebtedness.
What is the equation of the regression line (if applicable)?
Y=38672.0437+2.0793*X
Find y` when X = 4500 Median Grants.
When x=4500,
Y=38672.0437+2.0793*4500 = $48028.89
Regression Analysis
r²
0.506
n
8
r
0.711
k
1
Std. Error
5078.461
Dep. Var.
Avg. Indebt, Y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
158,563,498.4978
1
158,563,498.4978
6.15
.0478
Residual
154,744,607.5022
6
25,790,767.9170
Total
313,308,106.0000
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=6)
p-value
95% lower
95% upper
Intercept
38,672.0437
3,600.3929
10.741
3.85E-05
29,862.1997
47,481.8877
Median Grant, X
2.0793
0.8386
2.480
.0478
0.0274
4.1313
Predicted values for: Avg. Indebt, Y
95% Confidence Interval
95% Prediction Interval
Median Grant, X
Predicted
lower
upper
lower
upper
Leverage
4,500
48,029.016
43,354.074
52,703.958
34,752.189
61,305.844
0.142
Regression Analysis
r²
0.506
n
8
r
0.711
k
1
Std. Error
5078.461
Dep. Var.
Avg. Indebt, Y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
158,563,498.4978
1
158,563,498.4978
6.15
.0478
Residual
154,744,607.5022
6
25,790,767.9170
Total
313,308,106.0000
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=6)
p-value
95% lower
95% upper
Intercept
38,672.0437
3,600.3929
10.741
3.85E-05
29,862.1997
47,481.8877
Median Grant, X
2.0793
0.8386
2.480
.0478
0.0274
4.1313
Predicted values for: Avg. Indebt, Y
95% Confidence Interval
95% Prediction Interval
Median Grant, X
Predicted
lower
upper
lower
upper
Leverage
4,500
48,029.016
43,354.074
52,703.958
34,752.189
61,305.844
0.142
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