. Conduct t-tests on each of the beta parameters. What is your conclusion in each case? 1. What percentage of the variation in the price is explained by these independent variables'

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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c and d

a. State the null and alternative hypothesis in this global test for linear model utility.
b. Give the p-value and your conclusion.
c. Conduct t-tests on each of the beta parameters. What is your conclusion in each case?
d. What percentage of the variation in the price is explained by these independent variables?
Based on this, is a multiple linear regression model a good model for these data? Explain.
Transcribed Image Text:a. State the null and alternative hypothesis in this global test for linear model utility. b. Give the p-value and your conclusion. c. Conduct t-tests on each of the beta parameters. What is your conclusion in each case? d. What percentage of the variation in the price is explained by these independent variables? Based on this, is a multiple linear regression model a good model for these data? Explain.
B
F
G
K
M
N
1 Square Feet Sum of Bedrooms and Bathrooms
Sales Price
Square Feet Residual Plot
Square Feet Line Fit Plot
2
1,610
227,900
284,900
149,900
3
2,146
100000
800,000
4
816
4
700.000
5
2,183
6.5
309,900
50000
600,000
500.000
6
1,046
5.5
134,900
400,000
5,183
1,150
10.5
440,000
L,000
300,000
8
4
150,000
2,000
3,000
4,000
5,000
6.000
200,000
-50000
154,900
700,000
9
1,068
5
100,000
10
5,570
11
2,449
6
257,000
-100000
1,000
2,000
3,000
4,000
5,000
6,000
Square Feet
12
1,950
239,900
Square Feet
2,630
2,732
13
7.5
349,900
14
7.5
339,900
Sum of Bedrooms and Bathrooms
Sum of Bedrooms and Bathrooms Line
15
1,908
289,000
16
3,666
6.5
399,900
Residual Plot
Fit Plot
17
1,878
7
290,000
100000
18
2,172
7
278,000
800,000
19
50000
600,000
20 MMARY OUTPUT
400,000
21
8
10
12
200,000
ression Statistics
23 Multiple R
-50000
0.949278954
-100000
2
4
6
10
12
R Square
25 ljusted R Squa
26 tandard Erro
27 Observations
24
0.901130532
Sum of Bedrooms and Bathrooms
Sum of Bedrooms and Bathrooms
0.887006322
45879.39321
17
Normal Probability Plot
28
29
ANOVA
800000
30
df
SS
MS
Significance F
31 Regression
2
2.68589E+11
1.34295E+11
63.80042133
9.23497E-08
600000
32
Residual
14
29468862100 2104918721
400000
33
Total
16
2.98058E+11
200000
34
Upper 95%
259075.9965
Lower 95%
Coefficients
147150.7064
35
Standard Error
t Stat
P-value
Lower 95.0%
Upper 95.0%
36
Intercept
52184.81198 2.819799494
0.013638117
35225.41639
35225.41639
259075.9965
20
40
60
80
100
120
37 Square Feet
38 drooms and E
111.8732138
12.87582457 8.688625194
5.17078E-07
84.25731663
139.4891109
84.25731663
139.4891109
Sample Percentile
-18673.40799
11045.48378 -1.690592133
0.113047191
-42363.61457
5016.798593
-42363.61457
5016.798593
39
40
41
42 SIDUAL OUTPUT
PROBABILITY OUTPUT
43
44 Observation
Predicted Sales Price
Residuals
andard Residuals
Percentile
Sales Price
45
1
233899.5407
-5999.540663 -0.139796504
2.941176471
134900
46
2
275190.1753
9709.824745 0.226250579
8.823529412
149900
47
3
163745.6169
-13845.61692 -0.322619504
14.70588235
150000
48
4
269992.7802
39907.21983 0.929886155
20.58823529
154900
49
5
161466.3441
-26566.3441 -0.619027726
26.47058824
227900
50
6
530918.7895
-90918.78953 -2.118516999
32.35294118
239900
51
7
201111.2703
-51111.27032 -1.190953988
38.23529412
257000
52
8
173264.2588
-18364.2588 -0.427909287
44.11764706
278000
53
9
639570.6512
60429.34878 1.408076408
50
284900
54
10
309087.759
-52087.75903 -1.213707348
55.88235294
289000
55
11
234589.6174
5310.382633 0.123738294
61.76470588
290000
56
12
301326.6987
48573.30126
1.131816261
67.64705882
309900
57
13
312737.7665
27162.23346 0.632912664
73.52941176
339900
58
14
267237.7584
21762.24163 0.507086369
79.41176471
349900
59
15
435900.7562
-36000.75619 -0.83886086
85.29411765
399900
60
16
226534.746
63465.25402 1.478816647
91.17647059
440000
61
17
259425.4708
18574.52918 0.43280884
97.05882353
700000
62
Residuals
Sales Price
Sales Price
Sales Price
Transcribed Image Text:B F G K M N 1 Square Feet Sum of Bedrooms and Bathrooms Sales Price Square Feet Residual Plot Square Feet Line Fit Plot 2 1,610 227,900 284,900 149,900 3 2,146 100000 800,000 4 816 4 700.000 5 2,183 6.5 309,900 50000 600,000 500.000 6 1,046 5.5 134,900 400,000 5,183 1,150 10.5 440,000 L,000 300,000 8 4 150,000 2,000 3,000 4,000 5,000 6.000 200,000 -50000 154,900 700,000 9 1,068 5 100,000 10 5,570 11 2,449 6 257,000 -100000 1,000 2,000 3,000 4,000 5,000 6,000 Square Feet 12 1,950 239,900 Square Feet 2,630 2,732 13 7.5 349,900 14 7.5 339,900 Sum of Bedrooms and Bathrooms Sum of Bedrooms and Bathrooms Line 15 1,908 289,000 16 3,666 6.5 399,900 Residual Plot Fit Plot 17 1,878 7 290,000 100000 18 2,172 7 278,000 800,000 19 50000 600,000 20 MMARY OUTPUT 400,000 21 8 10 12 200,000 ression Statistics 23 Multiple R -50000 0.949278954 -100000 2 4 6 10 12 R Square 25 ljusted R Squa 26 tandard Erro 27 Observations 24 0.901130532 Sum of Bedrooms and Bathrooms Sum of Bedrooms and Bathrooms 0.887006322 45879.39321 17 Normal Probability Plot 28 29 ANOVA 800000 30 df SS MS Significance F 31 Regression 2 2.68589E+11 1.34295E+11 63.80042133 9.23497E-08 600000 32 Residual 14 29468862100 2104918721 400000 33 Total 16 2.98058E+11 200000 34 Upper 95% 259075.9965 Lower 95% Coefficients 147150.7064 35 Standard Error t Stat P-value Lower 95.0% Upper 95.0% 36 Intercept 52184.81198 2.819799494 0.013638117 35225.41639 35225.41639 259075.9965 20 40 60 80 100 120 37 Square Feet 38 drooms and E 111.8732138 12.87582457 8.688625194 5.17078E-07 84.25731663 139.4891109 84.25731663 139.4891109 Sample Percentile -18673.40799 11045.48378 -1.690592133 0.113047191 -42363.61457 5016.798593 -42363.61457 5016.798593 39 40 41 42 SIDUAL OUTPUT PROBABILITY OUTPUT 43 44 Observation Predicted Sales Price Residuals andard Residuals Percentile Sales Price 45 1 233899.5407 -5999.540663 -0.139796504 2.941176471 134900 46 2 275190.1753 9709.824745 0.226250579 8.823529412 149900 47 3 163745.6169 -13845.61692 -0.322619504 14.70588235 150000 48 4 269992.7802 39907.21983 0.929886155 20.58823529 154900 49 5 161466.3441 -26566.3441 -0.619027726 26.47058824 227900 50 6 530918.7895 -90918.78953 -2.118516999 32.35294118 239900 51 7 201111.2703 -51111.27032 -1.190953988 38.23529412 257000 52 8 173264.2588 -18364.2588 -0.427909287 44.11764706 278000 53 9 639570.6512 60429.34878 1.408076408 50 284900 54 10 309087.759 -52087.75903 -1.213707348 55.88235294 289000 55 11 234589.6174 5310.382633 0.123738294 61.76470588 290000 56 12 301326.6987 48573.30126 1.131816261 67.64705882 309900 57 13 312737.7665 27162.23346 0.632912664 73.52941176 339900 58 14 267237.7584 21762.24163 0.507086369 79.41176471 349900 59 15 435900.7562 -36000.75619 -0.83886086 85.29411765 399900 60 16 226534.746 63465.25402 1.478816647 91.17647059 440000 61 17 259425.4708 18574.52918 0.43280884 97.05882353 700000 62 Residuals Sales Price Sales Price Sales Price
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