Least Squares Point Estimates for Exercise 14.51 Bo = 10.3676 (.3710) B1 = .0500 (<.001) B2 = 6.3218 (.0152) B3 = -11.1032 (.0635) B4 = -.4319 (.0002) Questions Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05?
Least Squares Point Estimates for Exercise 14.51 Bo = 10.3676 (.3710) B1 = .0500 (<.001) B2 = 6.3218 (.0152) B3 = -11.1032 (.0635) B4 = -.4319 (.0002) Questions Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Table 14.17
The Least Squares Point Estimates for Exercise 14.51
Bo = 10.3676 (.3710)
B1 = .0500 (<.001)
B2 = 6.3218 (.0152)
B3 = -11.1032 (.0635)
B4 = -.4319 (.0002)
Questions
- Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05?
- Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .01. Which independent variables are significantly related to y in the model with α = .01?
- Find the p-value for testing Ho: βj = 0 versus Ha: βj ≠ 0 on the output. Using the p-value, determine whether we can reject Ho by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the independent variables in the model?
- Calculate the 95 percent confidence interval for βj. Discuss one practical application of this interval.
- Calculate the 99 percent confidence interval for βj.

Transcribed Image Text:13.10
Measurements Taken on 63 Single-Family Residences (for Exercise 13.57) OxHome
Sales
Price, y
Residence (x $1,000) x,
Square
Feet,
Sales
Price, y
Residence (x $1,000) x,
Rooms, Bedrooms, Age.
Square
Feet,
Rooms, Bedrooms, Age.
X2
1
53.5
1,008
2.
2
35
33
63.0
1,053
49.0
1,290
6
3
24
36
34
60.0
1,728
3
50.5
860
8
25
2
36
35
34.0
416
4
49.9
912
42
41
36
52.0
1,040
5
52.0
1,204
6
40
37
75.0
1,496
3.
6
55.0
1,204
30
3.
10
38
93.0
1,936
8
4
7.
80.5
1,764
8
39
4
39
60.0
1,904
1,080
64
32
86.0
1,600
7
3.
19
40
73.0
5
24
69.0
1,255
3.
16
41
71.0
1,768
8
4
74
10
200.
149.0
3,600
10
42
83.0
1,503
1,736
17
6
14
11
46.0
864
37
90.0
43
16
12
38.0
720
83.0
4
41
44
1,695
6.
12
13
49.5
1,008
6.
3.
35
45
115.0
2,186
8
12
14
105.0
1,950
8
52
46
50.0
888
2
34
15
152.5
2,086
12
47
55.2
1,120
3.
29
16
85.0
2,011
4
76
48
61.0
1,400
33
17
60.0
1,465
6.
3
102
49
147.0
2,165
18
58.5
1,232
5 2
69
50
210.0
2,353
8.
15
19
101.0
1,736
3
67
51
60.0
1,536
35
20
79.4
1,296
6.
11
52
100.0
1,972
37
21
125.0
1,996
3.
9.
53
44.5
1,120
27
22
87.9
1,874
2
14
54
55.0
1,664
7.
3
79
23
80.0
1,580
5
11
55
53.4
925
20
24
94.0
1,920
3
14
56
65.0
1,288
5.
25
74.0
1,430
9 3
16
57
73.0
1,400
2
1,486
3
27
58
40.0
1,376
103
26
69.0
6.
1,008
2.
35
59
141.0
2,038
12
62
27
63.0
67.5
1,282
3
20
60
68.0
1,572
29
28
29
35.0
1,134
74
61
139.0
1,545
62
140.0
1,993
1,130
30
142.5
2,400
9.
4
15
6.
21
3
15
63
55.0
2.
92.2
1,701
31
3.
16
56.0
1,020
32

Transcribed Image Text:Supplementary Exercises
The trend in home building in recent years has been to emphasize open spaces and great roome
14.51
community of Oxford, Ohio, had been building such homes, but his homes had been taking ge
months to sell and selling for substantially less than the asking price. In order to determine wube
types of homes would attract residents of the community, the builder contacted a statistician
at a local college. The statistician went to a local real estate agency and obtained the data in
Table 13.10 on page 518. This table presents the sales price y, square footage x, number of
rooms x, number of bedrooms x3, and age x4 for each of 63 single-family residences recently
sold in the community. When we perform a regression analysis of these data using the model
y= B, + Bjx, + Bx2 + Bzx3 + BX4 + ɛ
we find that the least squares point estimates of the model parameters and their associated
p-values (given in parentheses) are as shown in Table 14.17. Discuss why the estimates b. -
6.3218 and ba
specified square footage (1) to include both a (smaller) living room and family room rather than a
(larger) great room and (2) to not increase the number of bedrooms (at the cost of another type of
room) that would normally be included in a house of the specified square footage. Note: Based
on the statistical results, the builder realized that there are many families with children in a col-
lege town and that the parents in such families would rather have one living area for the children
(the family room) and a separate living area for themselves (the living room). The builder started
modifying his open-space homes accordingly and greatly increased his profits.
= -11.1032 suggest that it might be more profitable when building a house of a
OS OxHome
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