. How well can a students GPA at the end of the freshman year atcollege be predi
ID: 2914472 • Letter: #
Question
. How well can a students GPA at the end of the freshman year atcollege be predicted on the basis of his or her high school GPA?Eleven students were selected at random from a given college andtheir High School GPAs and their freshman year GPAs were collected.A simple linear regression model was fit by the method of leastsquares with the freshman GPA as the dependent variable(Y).
A subsequent article reports the values of the dependentvariable Y and the corresponding fitted values based onthe simple linear regression fit. However, the values of theindependent variable X (High School GPA) were notreported.
We want to perform a test of hypothesis to determine if theregression effect is significant. Is the data reported in the nexttable sufficient to perform this test? If so, test the hypothesis,report the necessary statistics and state your conclusion.
Student
Freshman GPA
Fits (From the Simple linear regression model
1
1.60
1.713
2
2.00
1.895
3
1.80
2.149
4
2.80
2.186
5
2.10
2.295
6
2.00
2.513
7
2.65
2.368
8
2.25
2.623
9
2.60
2.659
10
3.00
2.877
11
3.10
2.623
Student
Freshman GPA
Fits (From the Simple linear regression model
1
1.60
1.713
2
2.00
1.895
3
1.80
2.149
4
2.80
2.186
5
2.10
2.295
6
2.00
2.513
7
2.65
2.368
8
2.25
2.623
9
2.60
2.659
10
3.00
2.877
11
3.10
2.623
Explanation / Answer
Analysis ofVariance
Source DF SS MS F P
Regression 1 1.2337 1.2337 8.62 0.017
Residual Error 9 1.2886 0.1432
Total 10 2.5223
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