Solve the following problems:
1. 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
|
|
|
|
|
2.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
|
3. 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
|