In: Statistics and Probability
The file HW_05.xlsx contains data from a survey of 105 randomly selected households.
a. Interpret the ANOVA table for this model. In particular, does this set of independent variables provide at least some power in explaining the variation in the dependent variable? Report the F ratio statistics and p- value for this hypothesis test.
b. Interpret coefficients of independent variables in the model.
c. Using the regression output, determine which of the independent variables should be excluded from the regression equation. Justify your choices.
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.720892391 | |||||||
R Square | 0.519685839 | |||||||
Adjusted R Square | 0.490278849 | |||||||
Standard Error | 276.7505458 | |||||||
Observations | 105 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 6 | 8121168.832 | 1353528.139 | 17.67218775 | 8.86712E-14 | |||
Residual | 98 | 7505904.73 | 76590.86459 | |||||
Total | 104 | 15627073.56 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 2374.069071 | 926.2605378 | 2.563068353 | 0.011895868 | 535.9351797 | 4212.202963 | 535.9351797 | 4212.202963 |
Family Size | 4.840418883 | 36.07766888 | 0.13416662 | 0.893545971 | -66.75454085 | 76.43537862 | -66.75454085 | 76.43537862 |
Ownership | 702.453971 | 254.1314117 | 2.764136737 | 0.006819009 | 198.1384553 | 1206.769487 | 198.1384553 | 1206.769487 |
First Income | 0.003873026 | 0.003969221 | 0.975764656 | 0.331583598 | -0.004003765 | 0.011749817 | -0.004003765 | 0.011749817 |
Second Income | -0.001647966 | 0.00390663 | -0.421838302 | 0.674066972 | -0.009400547 | 0.006104614 | -0.009400547 | 0.006104614 |
Utilities | -9.501699186 | 4.780520124 | -1.987586903 | 0.049647926 | -18.98848579 | -0.014912585 | -18.98848579 | -0.014912585 |
Debt | 0.075526964 | 0.031183362 | 2.422027588 | 0.017272247 | 0.013644596 | 0.137409332 | 0.013644596 | 0.137409332 |
RESIDUAL OUTPUT | ||||||||
Observation | Predicted Monthly Payment | Residuals | ||||||
1 | 1283.656875 | 301.343125 | ||||||
2 | 811.8650323 | 502.1349677 | ||||||
3 | 740.136117 | -357.136117 | ||||||
4 | 664.9109715 | 78.08902852 | ||||||
5 | 772.8995857 | 218.1004143 | ||||||
6 | 750.3803306 | 240.6196694 | ||||||
7 | 644.4950874 | -25.49508743 | ||||||
8 | 725.8370344 | 271.1629656 | ||||||
9 | 881.904887 | 20.09511304 | ||||||
10 | 1282.983703 | -379.9837033 | ||||||
11 | 928.0753599 | -354.0753599 | ||||||
12 | 1210.663024 | 196.3369758 | ||||||
13 | 1285.798745 | -586.7987449 | ||||||
14 | 1099.112903 | -111.1129029 | ||||||
15 | 547.9950923 | 198.0049077 | ||||||
16 | 1245.445513 | 264.554487 | ||||||
17 | 1312.700688 | -221.7006883 | ||||||
18 | 571.6552022 | -169.6552022 | ||||||
19 | 595.4694334 | 100.5305666 | ||||||
20 | 1400.337463 | 147.6625366 | ||||||
21 | 1092.880423 | -173.8804234 | ||||||
22 | 1274.717884 | 394.2821161 | ||||||
23 | 1201.313724 | -152.3137235 | ||||||
24 | 973.0428122 | -480.0428122 | ||||||
25 | 1039.080963 | -317.0809633 | ||||||
26 | 1257.141849 | 166.8581514 | ||||||
27 | 1092.068254 | 365.9317455 | ||||||
28 | 858.0154957 | 118.9845043 | ||||||
29 | 1159.382074 | -97.38207423 | ||||||
30 | 1272.201934 | 387.7980659 | ||||||
31 | 696.6014074 | 2.398592648 | ||||||
32 | 957.713766 | -384.713766 | ||||||
33 | 897.0284126 | -149.0284126 | ||||||
34 | 1197.272226 | 120.7277742 | ||||||
35 | 557.7548128 | 14.2451872 | ||||||
36 | 578.1809184 | 90.81908161 | ||||||
37 | 1279.353171 | -7.353170783 | ||||||
38 | 1163.965973 | -79.96597284 | ||||||
39 | 1316.604504 | 159.3954956 | ||||||
40 | 745.0104365 | 287.9895635 | ||||||
41 | 830.7975511 | -310.7975511 | ||||||
42 | 883.7911442 | -382.7911442 | ||||||
43 | 1286.382047 | 5.617952509 | ||||||
44 | 528.6061347 | -38.60613475 | ||||||
45 | 1156.177396 | 278.8226044 | ||||||
46 | 1352.732087 | -229.7320871 | ||||||
47 | 1296.715593 | -3.715593069 | ||||||
48 | 763.0973175 | 12.90268253 | ||||||
49 | 1404.895087 | -529.8950867 | ||||||
50 | 1333.792182 | 200.2078182 | ||||||
51 | 1321.650183 | -38.65018315 | ||||||
52 | 1192.163015 | 109.8369849 | ||||||
53 | 962.8688489 | -322.8688489 | ||||||
54 | 1211.466446 | -222.4664463 | ||||||
55 | 1368.817034 | 382.1829664 | ||||||
56 | 750.0197314 | -322.0197314 | ||||||
57 | 665.7799644 | 222.2200356 | ||||||
58 | 1378.328756 | 90.6712441 | ||||||
59 | 1162.690779 | -219.6907794 | ||||||
60 | 877.1829337 | 256.8170663 | ||||||
61 | 1124.189015 | 153.8109847 | ||||||
62 | 1104.8985 | -90.89850046 | ||||||
63 | 1522.536888 | -385.5368878 | ||||||
64 | 1282.782166 | -451.7821656 | ||||||
65 | 780.9514237 | -202.9514237 | ||||||
66 | 1071.242456 | -31.24245591 | ||||||
67 | 692.164364 | -90.16436399 | ||||||
68 | 799.0201015 | -177.0201015 | ||||||
69 | 721.4005698 | -153.4005698 | ||||||
70 | 713.3984386 | -183.3984386 | ||||||
71 | 1238.49963 | 11.50037036 | ||||||
72 | 1212.513585 | 87.48641507 | ||||||
73 | 679.6402337 | -103.6402337 | ||||||
74 | 1057.642086 | 673.3579144 | ||||||
75 | 1030.391677 | -360.3916768 | ||||||
76 | 1275.455075 | 400.5449252 | ||||||
77 | 1093.559274 | -458.5592735 | ||||||
78 | 1234.956096 | -185.9560963 | ||||||
79 | 1253.486509 | 334.5134913 | ||||||
80 | 677.5991373 | -22.59913725 | ||||||
81 | 1090.956117 | 409.0438825 | ||||||
82 | 593.1143609 | 64.88563907 | ||||||
83 | 762.1428682 | -73.14286822 | ||||||
84 | 1062.675339 | -98.67533881 | ||||||
85 | 693.4603566 | -107.4603566 | ||||||
86 | 1192.488909 | 10.51109074 | ||||||
87 | 628.845734 | 133.154266 | ||||||
88 | 549.0101359 | 76.98986411 | ||||||
89 | 1355.011527 | 815.9884726 | ||||||
90 | 1309.5085 | -499.5084997 | ||||||
91 | 1345.31062 | 114.6893801 | ||||||
92 | 750.2098958 | 27.79010421 | ||||||
93 | 670.9580119 | -112.9580119 | ||||||
94 | 515.0339442 | 164.9660558 | ||||||
95 | 1196.856032 | -189.8560323 | ||||||
96 | 1066.47424 | 185.5257602 | ||||||
97 | 1474.366915 | -7.366915322 | ||||||
98 | 702.4299074 | 145.5700926 | ||||||
99 | 623.2275684 | 459.7724316 | ||||||
100 | 1326.672997 | 143.3270026 | ||||||
101 | 616.2223025 | -116.2223025 | ||||||
102 | 1156.731836 | -165.7318358 | ||||||
103 | 843.6802517 | -255.6802517 | ||||||
104 | 1435.944822 | 101.0551778 | ||||||
105 | 1129.731263 | 471.2687372 | ||||||