Question

In: Statistics and Probability

The file HW_05.xlsx contains data from a survey of 105 randomly selected households. a. Interpret the...

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

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