2 In the simple linear regression model y = Bo + Bjx + u, suppose that E(u) + 0. Letting a, = E(u),show that the model can always be rewritten with the same slope, but a new intercept and error, wherethe new error has a zero expected value.3 The following table contains the ACT scores and the GPA (grade point average) for eight college stu-dents. Grade point average is based on a four-point scale and has been rounded to one digit after thedecimal.StudentGPAACT12.82123.42433.02643.5273.62963.02572.7253.730(i)Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept andslope estimates in the equationGPA = B, + B¡ACT.Comment on the direction of the relationship. Does the intercept have a useful interpretationhere? Explain. How much higher is the GPA predicted to be if the ACT score is increased byfive points?(ii) Compute the fitted values and residuals for each observation, and verify that the residuals(approximately) sum to zero.

PLEASE NOTE AS PER THE BARTLEYBY POLICY I AM SOLVING FIRST QUESTION. PLEASE POST ANOTHER QUESTION…

2 In the simple linear regression model y = Bo + Bjx + u, suppose that E(u) # 0. Letting a, = E(u), show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value.

2 In the simple linear regression model y = Bo + Bjx + u, suppose that E(u) # 0. Letting a, = E(u), show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value.

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Chapter1: Making Economics Decisions

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Question

2 In the simple linear regression model y = Bo + Bjx + u, suppose that E(u) + 0. Letting a, = E(u),
show that the model can always be rewritten with the same slope, but a new intercept and error, where
the new error has a zero expected value.
3 The following table contains the ACT scores and the GPA (grade point average) for eight college stu-
dents. Grade point average is based on a four-point scale and has been rounded to one digit after the
decimal.
Student
GPA
ACT
1
2.8
21
2
3.4
24
3
3.0
26
4
3.5
27
3.6
29
6
3.0
25
7
2.7
25
3.7
30
(i)
Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and
slope estimates in the equation
GPA = B, + B¡ACT.
Comment on the direction of the relationship. Does the intercept have a useful interpretation
here? Explain. How much higher is the GPA predicted to be if the ACT score is increased by
five points?
(ii) Compute the fitted values and residuals for each observation, and verify that the residuals
(approximately) sum to zero.

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