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Explain this objective in a regression model: How does UTILITY COST of household relate to (Housing Cost at 6 percent In...

Explain this objective in a regression model:
How does UTILITY COST of household relate to
(Housing Cost at 6 percent Interest, Median
Income Adjusted for # of Bedrooms, and
# of bedrooms in unit) Among Low Income People.

Data below

UTILITY COST06 ABLMED BEDRMS GLMED
169 648.5882 66364.2 2 73738 SUMMARY OUTPUT
245.3333 1167.641 64781.36 4 55846
159 1193.393 64781.36 4 55846 Regression Statistics
179 1578.858 58079.84 3 55846 Multiple R 0.589079
146 759 54891.9 2 60991 R Square 0.347014
94.75 695 46549.5 1 62066 Adjusted R Square 0.346984
236 2038.948 63430.64 3 60991 Standard Error 105.1893
81 976 47089.8 2 52322 Observations 64535
184.0833 1361.396 52307.84 3 50296
0 1100 47415.75 1 63221 ANOVA
172 1742.236 58079.84 3 55846 df SS MS F Significance F
467.5833 1871.774 82383.36 5 64362 Regression 3 3.79E+08 1.26E+08 11431.18 0
135 993 57925.8 2 64362 Residual 64531 7.14E+08 11064.79
152.1667 2220.953 66749.28 3 64182 Total 64534 1.09E+09
364 2919.879 74451.12 4 64182
469.8333 2574.62 82383.36 5 64362 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
50.08333 600 50261.4 2 55846 Intercept -10.0181 1.827855 -5.48082 4.25E-08 -13.6007 -6.43555 -13.6007 -6.43555
332.8333 1907.236 80668.64 3 77566 COST06 0.01641 0.000274 59.88312 0 0.015873 0.016947 0.015873 0.016947
245.6667 1280.06 65936 3 63400 ABLMED 0.000406 3.47E-05 11.70137 1.35E-31 0.000338 0.000474 0.000338 0.000474
145.1667 2213.953 62550 2 69500 BEDRMS 52.92576 0.49346 107.2544 0 51.95858 53.89294 51.95858 53.89294
65 503.7573 53240.4 2 59156
109 383.5882 50890.5 2 56545
141.8333 2164.994 53240.4 2 59156
math   Statistics-And-Probability   
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Homework Answers

Answer #1

From the regression output we obtain the following model

UTILITY COST=-10.0181 + 0.01641*COSAT06 + 0.000406*AMBLED + 52.92576*BEDRMS

To test the significance of the overall model we find the out put of F test which gives the F value as 11431.18 and the p value =0 < 0.05 .Hence the model is overall significant.

R square value is 0.347014, which 34.7% of the total variation in the independent variables is explained by the regression model.

The p value of the t test for individual regression for all individual independent variable is < 0.05 which suggest that all the independent variables including the intercept is significant.

For any further clarifications please comment

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