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. e) Give the point estimate for the price of a 44 year old single family home in Beavercreek, OH

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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d and e

Square Feet
Sum of Bedrooms and Bathrooms Age of the Home
Sales Price
Square Feet Residual Plot
Square Feet Line Fit Plot
1,610
5
70
227,900
800,000
2,146
6
59
284,900
700,000
816
4
70
149,900
600,000
2,183
6.5
48
309,900
40000
1,046
5.5
64
134,900
500.000
20000
5,183
10.5
21
440,000
400,000
• 2 000
1,150
4
62
150,000
1,000
4,000
5.000
6,000
2000 0
300,000
1,068
70
154,900
4000 0
5,570
7
50
700,000
200,000
6000 0
2,449
6.
53
257,000
100,000
BO00 O
1,950
59
239,900
1000 00
2,630
7.5
73
349,900
Square Feet
1,000
2,000
3,000
4,000
5,000
6,000
Square Feet
2,732
7.5
20
339,900
1,908
46
289,000
3,666
6.5
17
399,900
Sum of Bedrooms and Bathrooms Residual Plot
Sum of Bedrooms and Bathrooms Line Fit Plot
80000
1,878
7
19
290,000
800,000
2,172
62
278,000
60000
700,000
40000
600,000
SUMMARY OUTPUT
20000
500,000
400,000
Regression Statistics
12
2000 0
Multiple R
0.949366054
300,000
R Square
0.901295904
4000 0
200,000
Adjusted R Square
0.878518035
6000 0
100,000
Standard Error
47571,46177
8000 0
Observations
17
2
12
1000 00
Sum of Bedrooms and Bathrooms
Sum of Bedrooms and Bathrooms
ANOVA
df
SS
MS
F
Significance F
Age of the Home Residual Plot
Age of the Home Line Fit Plot
Regression
2.68639E+11
8.9546E+1039.5689
8,44E-07
80000
800,000
Residual
13
29419571670 2263043975
700.000
Total
16
2.98058E+11
40000
20000
500,000
Lower 95% Upper 95%ɔwer 95.0spper 95.0
t Stat
1.588278630.13624 -49422.95889 323846
Coefficients
Standard Error
P-value
86390.17753
-49423
323846
400,000
Intercept
137211.6729
10
20
60
80
Square Feet
13.62585831
2000 0
112.2753036
8.23987018 1.62E-06 82.83842641 141.712 82.8384 141.712
300,000
of Bedrooms and Bathro
-18138.453
12012.77866
-1.50992984 0.15498 -44090.48349 7813.58
-44090
7813.58
4000 0
200,000
Age of the Home
110.7493211
750.4232224
0.14758248
0.88494 -1510.441488 1731.94
-1510.4 1731.94
100,000
8000 0
80
1000 00
Age of the Home
Age of the Home
RESIDUAL OUTPUT
PROBABILITY OUTPUT
Normal Probability Plot
Observation
Predicted Sales Price
Residuals
indard Residuals
Percentile
Sales Price
800000
1
235035.0992
-7135.099201
-0.1663956
2,941176471 134900
700000
275857.9664
9042.033582
0.21086667
8.823529412
149900
3
164026.9611
-14126.96112
-0.3294508
14.70588235
150000
4
269724.6836
40175.31638
0.93691701
20.58823529
154900
So000
5
161978.1055
-27078.10553
-0.63148072
26.47058824
227900
6.
531006.5509
-91006.55085 -2.12233763
32.35294118
239900
7
200640.918
-50640.91796
-1.1809823
38.23529412
257000
300000
8
174181.8846
-19281.88463 -0.44966729
44.11764706 278000
200000
641153.4092
58846.59085
1.37234444
50
284900
10
309212.8875
-52212.88749
-1.21764175
55.88235294
289000
100000
11
235713.5539
4186.446089
0.09763091
61.76470588
290000
12
304542.0244
45357.97562
1.05778032
67.64705882
309900
20
40
60
80
100
120
Sample Percentile
13
310124.3913
29775.60867
0.69438842
73.52941176
339900
14
265835.156
23164.84402
0.54022067
79.41176471
349900
15
432795.7299
-32895.72995
-0.76715187
85.29411765
399900
16
223199.7592
66800.24079
1.55782922
91.17647059
440000
17
260970.9193
17029.08072
0.3971303
97.05882353
700000
Transcribed Image Text:Square Feet Sum of Bedrooms and Bathrooms Age of the Home Sales Price Square Feet Residual Plot Square Feet Line Fit Plot 1,610 5 70 227,900 800,000 2,146 6 59 284,900 700,000 816 4 70 149,900 600,000 2,183 6.5 48 309,900 40000 1,046 5.5 64 134,900 500.000 20000 5,183 10.5 21 440,000 400,000 • 2 000 1,150 4 62 150,000 1,000 4,000 5.000 6,000 2000 0 300,000 1,068 70 154,900 4000 0 5,570 7 50 700,000 200,000 6000 0 2,449 6. 53 257,000 100,000 BO00 O 1,950 59 239,900 1000 00 2,630 7.5 73 349,900 Square Feet 1,000 2,000 3,000 4,000 5,000 6,000 Square Feet 2,732 7.5 20 339,900 1,908 46 289,000 3,666 6.5 17 399,900 Sum of Bedrooms and Bathrooms Residual Plot Sum of Bedrooms and Bathrooms Line Fit Plot 80000 1,878 7 19 290,000 800,000 2,172 62 278,000 60000 700,000 40000 600,000 SUMMARY OUTPUT 20000 500,000 400,000 Regression Statistics 12 2000 0 Multiple R 0.949366054 300,000 R Square 0.901295904 4000 0 200,000 Adjusted R Square 0.878518035 6000 0 100,000 Standard Error 47571,46177 8000 0 Observations 17 2 12 1000 00 Sum of Bedrooms and Bathrooms Sum of Bedrooms and Bathrooms ANOVA df SS MS F Significance F Age of the Home Residual Plot Age of the Home Line Fit Plot Regression 2.68639E+11 8.9546E+1039.5689 8,44E-07 80000 800,000 Residual 13 29419571670 2263043975 700.000 Total 16 2.98058E+11 40000 20000 500,000 Lower 95% Upper 95%ɔwer 95.0spper 95.0 t Stat 1.588278630.13624 -49422.95889 323846 Coefficients Standard Error P-value 86390.17753 -49423 323846 400,000 Intercept 137211.6729 10 20 60 80 Square Feet 13.62585831 2000 0 112.2753036 8.23987018 1.62E-06 82.83842641 141.712 82.8384 141.712 300,000 of Bedrooms and Bathro -18138.453 12012.77866 -1.50992984 0.15498 -44090.48349 7813.58 -44090 7813.58 4000 0 200,000 Age of the Home 110.7493211 750.4232224 0.14758248 0.88494 -1510.441488 1731.94 -1510.4 1731.94 100,000 8000 0 80 1000 00 Age of the Home Age of the Home RESIDUAL OUTPUT PROBABILITY OUTPUT Normal Probability Plot Observation Predicted Sales Price Residuals indard Residuals Percentile Sales Price 800000 1 235035.0992 -7135.099201 -0.1663956 2,941176471 134900 700000 275857.9664 9042.033582 0.21086667 8.823529412 149900 3 164026.9611 -14126.96112 -0.3294508 14.70588235 150000 4 269724.6836 40175.31638 0.93691701 20.58823529 154900 So000 5 161978.1055 -27078.10553 -0.63148072 26.47058824 227900 6. 531006.5509 -91006.55085 -2.12233763 32.35294118 239900 7 200640.918 -50640.91796 -1.1809823 38.23529412 257000 300000 8 174181.8846 -19281.88463 -0.44966729 44.11764706 278000 200000 641153.4092 58846.59085 1.37234444 50 284900 10 309212.8875 -52212.88749 -1.21764175 55.88235294 289000 100000 11 235713.5539 4186.446089 0.09763091 61.76470588 290000 12 304542.0244 45357.97562 1.05778032 67.64705882 309900 20 40 60 80 100 120 Sample Percentile 13 310124.3913 29775.60867 0.69438842 73.52941176 339900 14 265835.156 23164.84402 0.54022067 79.41176471 349900 15 432795.7299 -32895.72995 -0.76715187 85.29411765 399900 16 223199.7592 66800.24079 1.55782922 91.17647059 440000 17 260970.9193 17029.08072 0.3971303 97.05882353 700000
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.
e) Give the point estimate for the price of a 44 year old single family home in Beavercreek, OH
with 1704 square feet of living space, 3 bedrooms, and 2.5 bathrooms.
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. e) Give the point estimate for the price of a 44 year old single family home in Beavercreek, OH with 1704 square feet of living space, 3 bedrooms, and 2.5 bathrooms.
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