a. State the null and alternative hypothesis in this global test for linear model utility. b. Give the p-value and your conclusion.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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a and b

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
D
E
G
H
K
M
1 Square Feet Age of the Home Sales Price
Square Feet Residual Plot
Square Feet Line Fit Plot
2
1,610
70
227,900
3
2,146
284,900
149,900
59
100000
800,000
4
816
70
700,000
50000
600,000
5
2,183
48
309,900
500,000
6
1,046
64
134,900
400,000
5,183
21
440,000
1,000
2,000
3,000
4,000
5,000
6.000
300,000
-50000
8
1,150
62
150,000
200,000
100,000
9
1,068
70
154,900
-100000
10
5,570
50
700,000
-150000
1,000
2,000
3,000
4,000
5,000
6,000
11
2,449
53
257,000
Square Feet
12
1,950
59
239,900
Square Feet
2,630
2,732
13
73
349,900
14
20
339,900
Age of the Home Residual Plot
15
1,908
Age of the Home Line Fit Plot
289,000
399,900
46
100000
16
3,666
17
800,000
17
1,878
19
290,000
50000
18
2,172
62
278,000
600,000
19
20 MMARY OUTPUT
10
20
30
40
50
60.
70
80
400,000
-50000
21
200,000
-100000
ression Statistics
23 Multiple R
0.94020507
-150000
10
20
30
40
50
60
70
80
Age of the Home
R Square
25 ljusted R Squa 0.867412084
26 tandard Erro
24
0.883985573
Age of the Home
49698.41817
27 Observations
17
28
Normal Probability Plot
29
ANOVA
800000
30
df
S
MS
Significance F
31 Regression
2
2.63479E+11 1.3174E+11
53.33732344
2.82868E-07
600000
32
Residual
14
34579058765 2469932769
400000
33
Total
16
2.98058E+11
34
200000
Upper 95%
159992.9769
Standard Error
t Stat
Lower 95.0%
-86656.451
35
Coefficients
P-value
Lower 95%
Upper 95.0%
36
Intercept
36668.26295
57499.75727 0.63771161
0.533953161
-86656.451
159992.9769
20
40
60
80
100
120
37 Square Feet
38 ge of the Hon
99.16082372
10.96828321 9.04068776
3.20882E-07
75.6361959
122.6854515
75.6361959
122.6854515
Sample Percentile
452.6516011
747.433283 0.60560803
0.554466659
-1150.433354
2055.736556
-1150.433354
2055.736556
39
40
41
42 SIDUAL OUTPUT
PROBABILITY OUTPUT
43
44 Observation redicted Sales Pric
Residuals
indard Residuals
Percentile
Sales Price
45
1
228002.8012
-102.801216 -0.0022113
2.941176471
134900
46
2
276173.8351
8726.164883 0.18770542
8.823529412
149900
47
3
149269.1072
630.8928168 0.01357091
14.70588235
150000
48
4
274863.618
35036.38202 0.75365513
20.58823529
154900
49
5
169360.187
-34460.187
-0.7412608
26.47058824
227900
50
6
560124.4959
-120124.496
-2,5839552
32.35294118
239900
51
7
178767.6095
-28767.6095
-0.6188098
38.23529412
257000
52
8
174257.6348
-19357.6348
-0.4163952
44.11764706
278000
53
9
611626.6311
88373.36888 1.90096805
50
284900
54
10
303503.6551
-46503.6551 -1.0003236
55.88235294
289000
55
11
256738.3137
-16838.3137
-0.362203
61.76470588
290000
56
12
330504.7962
19395.20379 0.41720332
67.64705882
309900
57
13
316628.6654
23271.33463 0.50058139
73.52941176
339900
58
14
246689.0883
42310.91174 0.91013495
79.41176471
349900
59
15
407886.9199
-7986.91992
-0.1718038
85.29411765
399900
60
16
231492.6703
58507.32968 1.25853032
91.17647059
440000
61
17
280109.9713
-2109.97134 -0.0453868
97.05882353
700000
62
Residuals
Sales Price
Sales Price
Sales Price
Transcribed Image Text:B D E G H K M 1 Square Feet Age of the Home Sales Price Square Feet Residual Plot Square Feet Line Fit Plot 2 1,610 70 227,900 3 2,146 284,900 149,900 59 100000 800,000 4 816 70 700,000 50000 600,000 5 2,183 48 309,900 500,000 6 1,046 64 134,900 400,000 5,183 21 440,000 1,000 2,000 3,000 4,000 5,000 6.000 300,000 -50000 8 1,150 62 150,000 200,000 100,000 9 1,068 70 154,900 -100000 10 5,570 50 700,000 -150000 1,000 2,000 3,000 4,000 5,000 6,000 11 2,449 53 257,000 Square Feet 12 1,950 59 239,900 Square Feet 2,630 2,732 13 73 349,900 14 20 339,900 Age of the Home Residual Plot 15 1,908 Age of the Home Line Fit Plot 289,000 399,900 46 100000 16 3,666 17 800,000 17 1,878 19 290,000 50000 18 2,172 62 278,000 600,000 19 20 MMARY OUTPUT 10 20 30 40 50 60. 70 80 400,000 -50000 21 200,000 -100000 ression Statistics 23 Multiple R 0.94020507 -150000 10 20 30 40 50 60 70 80 Age of the Home R Square 25 ljusted R Squa 0.867412084 26 tandard Erro 24 0.883985573 Age of the Home 49698.41817 27 Observations 17 28 Normal Probability Plot 29 ANOVA 800000 30 df S MS Significance F 31 Regression 2 2.63479E+11 1.3174E+11 53.33732344 2.82868E-07 600000 32 Residual 14 34579058765 2469932769 400000 33 Total 16 2.98058E+11 34 200000 Upper 95% 159992.9769 Standard Error t Stat Lower 95.0% -86656.451 35 Coefficients P-value Lower 95% Upper 95.0% 36 Intercept 36668.26295 57499.75727 0.63771161 0.533953161 -86656.451 159992.9769 20 40 60 80 100 120 37 Square Feet 38 ge of the Hon 99.16082372 10.96828321 9.04068776 3.20882E-07 75.6361959 122.6854515 75.6361959 122.6854515 Sample Percentile 452.6516011 747.433283 0.60560803 0.554466659 -1150.433354 2055.736556 -1150.433354 2055.736556 39 40 41 42 SIDUAL OUTPUT PROBABILITY OUTPUT 43 44 Observation redicted Sales Pric Residuals indard Residuals Percentile Sales Price 45 1 228002.8012 -102.801216 -0.0022113 2.941176471 134900 46 2 276173.8351 8726.164883 0.18770542 8.823529412 149900 47 3 149269.1072 630.8928168 0.01357091 14.70588235 150000 48 4 274863.618 35036.38202 0.75365513 20.58823529 154900 49 5 169360.187 -34460.187 -0.7412608 26.47058824 227900 50 6 560124.4959 -120124.496 -2,5839552 32.35294118 239900 51 7 178767.6095 -28767.6095 -0.6188098 38.23529412 257000 52 8 174257.6348 -19357.6348 -0.4163952 44.11764706 278000 53 9 611626.6311 88373.36888 1.90096805 50 284900 54 10 303503.6551 -46503.6551 -1.0003236 55.88235294 289000 55 11 256738.3137 -16838.3137 -0.362203 61.76470588 290000 56 12 330504.7962 19395.20379 0.41720332 67.64705882 309900 57 13 316628.6654 23271.33463 0.50058139 73.52941176 339900 58 14 246689.0883 42310.91174 0.91013495 79.41176471 349900 59 15 407886.9199 -7986.91992 -0.1718038 85.29411765 399900 60 16 231492.6703 58507.32968 1.25853032 91.17647059 440000 61 17 280109.9713 -2109.97134 -0.0453868 97.05882353 700000 62 Residuals Sales Price Sales Price Sales Price
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