Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

The following table contains ACT scores and GPA (grade point average) scores for 8 college students. (The ACT is an SAT-type test, popular at Midwestern schools.
Instead of ranging from 200 – 800, the ACT ranges from 20 – 30.) Grade point average is based on a 4-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
5 3.6 29
6 3.0 25
7 2.7 25
8 3.7 30
i) Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and the slope estimates for the model
GPAi = α + β(ACTi) + μi
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 increases by 5 points?
ii) Compute the fitted values and the residuals for each observation and verify that the residuals sum to zero.
iii) What is the predicted value of GPA when ACT = 20?

Sagot :

fichoh

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

ACT (X) :

21

24

26

27

29

25

25

30

GPA (Y) :

2.8

3.4

3.0

3.5

3.6

3.0

2.7

3.7

Relationship between GPA and ACT using a linear regression calculator :

ŷ = 0.1022X + 0.56813

Slope = 0.1022

Intercept = 0.56813

The relationship between GPA and ACT is in the positive direction, this can be inferred from the slope value which is positive

The intercept value ; 0.56813 means with a GPA score of 0 ; predicted ACT score will be 0.56813

Explain. How much higher is the GPA predicted to be if the ACT score increases by 5 points?

If ACT score increases by 5 ; predicted GPA will be:

Increase = 0.1022(5)

ACT score will increases by 0.511

ii) Compute the fitted values and the residuals for each observation and verify that the residuals sum to zero.

y = 0.1022(21) + 0.56813 = 2.71433

y = 0.1022(24) + 0.56813 = 3.02093

y = 0.1022(26) + 0.56813 = 3.22533

y = 0.1022(27) + 0.56813 = 3.32753

y = 0.1022(29) + 0.56813 = 3.53193

y = 0.1022(25) + 0.56813 = 3.12313

y = 0.1022(25) + 0.56813 = 3.12313

y = 0.1022(30) + 0.56813 = 3.63413

Residual:

2.8 - 2.71433 = 0.08567

3.4 - 3.02093 = 0.37907

3.0 - 3.22533 = −0.22533

3.5 - 3.32753 = 0.17247

3.6 - 3.53193 = 0.06807

3.0 - 3.12313 = −0.12313

2.7 -3.12313 = −0.42313

3.7 - 3.63413 = 0.06587

0.08567+0.37907−0.22533+0.17247+0.06807−0.12313−0.42313+0.06587 = −0.00044 = 0.00

iii) What is the predicted value of GPA when ACT = 20?

ŷ = 0.1022(20) + 0.56813

= 2.61

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.