The following table contains the ACT scores and the GPA (Grade Point Average) fo
ID: 3041459 • Letter: T
Question
The following table contains the ACT scores and the GPA (Grade Point Average) for eight college students. GPA is based on 4 point scale with one decimal.
1
(a)Estimate the relationship netween the ACT and GPA by using OLS. That is obtain the intersept and slope estimates in the equation.
What is the direction of the relationship? Is the intercept a useful interperatiation here? Explain. How much higher is GPA predicted to be if ACT raises 5 points.
(b) Compute the fitted values and residuals for each observation and verify that the residuals (approxamiate) sum to zero.
student gpa act1
2.8 21 2 3.4 24 3 3.0 26 4 3.5 27 5 3.6 29 6 3.0 25 7 2.7 25 8 3.7 30Explanation / Answer
Answer:
(a)Estimate the relationship netween the ACT and GPA by using OLS. That is obtain the intersept and slope estimates in the equation.
GPA = 0.5681+0.1022*ACT
What is the direction of the relationship?
The relation is positive. (Regression coefficient is positive).
Is the intercept a useful interperatiation here?
No, 0 value of ACT score is out of range of ACT scores.
Explain. How much higher is GPA predicted to be if ACT raises 5 points.
5*0.1022 =0.511
if ACT raises 5 points then GPA increases by 0.511.
Regression Analysis
r²
0.577
n
8
r
0.760
k
1
Std. Error
0.269
Dep. Var.
gpa
ANOVA table
Source
SS
df
MS
F
p-value
Regression
0.5940
1
0.5940
8.20
.0287
Residual
0.4347
6
0.0725
Total
1.0288
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=6)
p-value
95% lower
95% upper
Intercept
0.5681
0.9284
0.612
.5630
-1.7036
2.8399
act
0.1022
0.0357
2.863
.0287
0.0149
0.1895
(b) Compute the fitted values and residuals for each observation and verify that the residuals (approxamiate) sum to zero.
Observation
gpa
Predicted
Residual
1
2.80
2.71
0.09
2
3.40
3.02
0.38
3
3.00
3.23
-0.23
4
3.50
3.33
0.17
5
3.60
3.53
0.07
6
3.00
3.12
-0.12
7
2.70
3.12
-0.42
8
3.70
3.63
0.07
Total
0.00
Regression Analysis
r²
0.577
n
8
r
0.760
k
1
Std. Error
0.269
Dep. Var.
gpa
ANOVA table
Source
SS
df
MS
F
p-value
Regression
0.5940
1
0.5940
8.20
.0287
Residual
0.4347
6
0.0725
Total
1.0288
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=6)
p-value
95% lower
95% upper
Intercept
0.5681
0.9284
0.612
.5630
-1.7036
2.8399
act
0.1022
0.0357
2.863
.0287
0.0149
0.1895
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