A mortgage department of a large bank is studying its recent loans. Of particula

Question

A mortgage department of a large bank is studying its recent loans. Of particular interest is how such factors as the value of the home (in thousands of dollars), education level of the head of the household, age of the head of the household, current monthly mortgage payment (in dollars), and gender of the head of the household (male = 1, female = 0) relate to the family income. Are these variables effective predictors of the income of the household? A random sample of 25 recent loans is obtained. (Round the final answers to 3 decimal places.)

Conduct a global hypothesis test to determine whether any of the independent variables are different from zero. Test at a significance level of 0.05.

Conduct individual hypothesis tests to determine whether any of the independent variables can be dropped. Test at a significance level of 0.05. (Negative answer should be indicated by a minus sign.)

A mortgage department of a large bank is studying its recent loans. Of particular interest is how such factors as the value of the home (in thousands of dollars), education level of the head of the household, age of the head of the household, current monthly mortgage payment (in dollars), and gender of the head of the household (male = 1, female = 0) relate to the family income. Are these variables effective predictors of the income of the household? A random sample of 25 recent loans is obtained. (Round the final answers to 3 decimal places.)

Explanation / Answer

a)

y = 19.5975 + 0.0447*x1 + 0.8494 *x2 -0.01644*x3 -0.0009235*x4 +1.68547*x5

b)

R^2 = 0.9547

hence 95.47 % of variation of y is explaned by this model

c)

d)

if p-value < 0.05 , the variable is significant

here x3 and x4 are not significant and can be removed

e)

y = 17.9766 + 0.04307 * x1 + 0.90672*x2 + 1.68029* x3

R^2 = 0.95265

SUMMARY OUTPUT Regression Statistics Multiple R 0.977110959 R Square 0.954745827 Adjusted R Square 0.942836834 Standard Error 0.524225069 Observations 25 ANOVA df SS MS F Significance F Regression 5 110.1585735 22.03171469 80.1701559 4.21414E-12 Residual 19 5.221426533 0.274811923 Total 24 115.38 Coefficients Standard Error t Stat P-value Lower 95% Intercept 19.5974961 4.700976604 4.168813791 0.000521109 9.758238986 Value 0.044713571 0.009046883 4.942428156 9.04188E-05 0.025778226 Education 0.849449967 0.347688329 2.443136268 0.024498251 0.121729931 -0.016443202 0.024819317 -0.662516276 0.515597299 -0.06839063 Payment -0.000923571 0.001811468 -0.509846426 0.616030423 -0.004715017 1.685471791 0.359395003 4.689747421 0.000159573 0.933249403

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