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Regression analysis for SAT score

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4-16 Thirteen students entered the undergraduate business program at Rollins College two years ago. The following table indicates what their grade-point averages (GPAs) were after being in the program for two years and what each student scored on one part of the SAT exam when he or she was in high school. Is there a meaningful relationship between grades and SAT scores? If a student scores a 450 on the SAT, what do you think his or her GPA will be? What about a student who scores 800?

Student SAT Score GPA Student SAT Score GPA
A 421 2.90 H 481 2.53
B 377 2.93 I 729 3.22
C 585 3.00 J 501 1.99
D 690 3.45 K 613 2.75
E 608 3.66 L 709 3.90
F 390 2.88 M 366 1.60
G 415 2.15

4-20 The following data give the selling price, square footage, number of bedrooms, and age of houses that have sold in a neighborhood in the last 6 months. Develop three regression models to predict the selling price base~ upon each of' the other factors individually. Which of these is best?

Selling Price Square Footage Bedrooms Age
64000 1670 2 30
59000 1339 2 25
61500 1712 3 30
79000 1840 3 40
87500 2300 3 18
92500 2234 3 30
95000 2311 3 19
113000 2377 3 7
115000 2736 4 10
138000 2500 3 1
142500 2500 4 3
144000 2479 3 3
145000 2400 3 1
147500 3124 4 0
144000 2500 3 2
155500 4062 4 10
165000 2854 3 3
4-25 A sample of twenty automobiles was taken, and the miles per gallon (MPG), horsepower, and total weight were recorded. Develop a linear regression model to predict MPG using horsepower as the only independent variable. Develop another model with weight as the independent variable. Which of these two models is better? Explain.

MPG Horsepower Weight
37 66 1797
34 63 2199
35 90 2404
32 99 2611
30 63 3236
28 91 2606
26 94 2580
26 88 2507
25 124 2922
22 97 2434
20 114 3248
21 102 2812
18 114 3382
18 142 3197
16 153 4380
16 139 4036

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The solution provides step by step method for the calculation of regression analysis. Formula for the calculation and Interpretations of the results are also included.

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