Use the file California Data.xls for the following questions. a. Regress Loan Am

Question

Use the file California Data.xls for the following questions.

a. Regress Loan Amount on income, black, other race, and male. Comment on the results using OLS.

b. Estimate the same model using quantile regression at the 50th percentile. How do your results in parts (a) and (b) differ?

c. Estimate the model at the 10th, 25th, 75th, and 90th percentiles. Do these results differ from the results you found in parts (a) and (b)?

d. From a policy perspective, why do you think it is important to not just focus on average values but also consider the marginal values at different points in the
distribution?

Loan Amt. App Inc Black Other Race Male 320 0 0 0 1 181 4 0 0 0 148 5 0 0 1 187 10 0 0 1 40 13 1 0 0 35 17 0 0 0 153 19 0 0 1 225 19 0 0 0 60 20 0 0 1 55 21 1 0 1 45 21 0 0 1 88 21 0 0 1 239 22 0 0 1 44 22 0 1 0 161 22 0 1 0 69 22 0 0 1 183 23 0 0 1 61 23 0 0 1 135 23 0 1 1 75 24 0 0 1 53 24 0 0 0 47 24 0 0 1 99 24 0 0 1 70 25 0 0 0 63 25 0 1 1 62 25 0 1 0 28 25 1 0 0 68 26 0 0 0 99 26 1 0 0 87 26 0 1 1 70 26 1 0 0 110 26 0 0 1 66 26 1 0 1 90 27 0 0 1 170 27 0 1 1 55 27 0 0 0 82 27 0 0 1 64 27 0 0 0 130 27 0 0 1 48 27 0 0 0 66 27 0 0 0 59 27 0 1 0 65 27 1 0 0 63 27 1 0 1 48 27 0 0 0 9 28 0 0 0 30 28 0 0 0 132 28 0 0 1 46 28 0 0 0 80 28 1 0 0 77 28 0 0 0 121 28 1 0 0 100 28 1 0 0 60 29 0 0 0 65 29 0 0 1 59 29 0 0 1 60 29 0 0 1 46 29 0 0 1 50 29 0 0 1 110 29 0 0 0 130 29 0 0 1 116 29 0 0 1 50 29 0 0 1 70 30 0 0 1 128 30 0 1 1 58 30 0 0 0 56 30 0 0 0 75 30 0 1 1 50 30 0 0 1 55 30 0 0 1 56 30 0 0 1 73 30 0 0 0 155 30 0 0 0 60 30 0 0 1 81 30 0 0 1 96 30 0 0 1 180 30 1 0 0 95 30 0 0 0 67 30 0 0 0 93 30 0 0 0 30 30 0 0 0 55 30 0 0 1 213 30 1 0 1 17 31 0 0 1 25 31 0 0 0 160 31 0 0 0 150 31 0 0 1 135 31 0 0 1 53 31 0 0 1 41 31 0 0 0 70 31 0 0 1 100 31 0 0 0 135 31 0 1 1 74 31 1 0 0 171 32 0 1 0 65 32 0 1 0 59 32 0 0 0 104 32 0 0 1 65 32 0 0 1 162 32 0 0 1 84 32 0 0 0 68 32 0 0 1 60 32 0 0 0 60 33 0 0 1 65 33 0 0 0 75 33 0 0 0 28 33 0 0 1 130 33 0 0 0 105 33 0 0 0 86 33 0 0 1 70 33 1 0 1 90 33 0 0 1 70 33 0 0 1 130 33 0 0 1

Explanation / Answer

(a)

From the given data,we find the Regress Loan Amount on income with black,other race and male from the excel sheet is given by

first we enter the data of Loan amount on income and black,other race and male then goto data->data anlysis->Click on Regression->slect the input Y(Loan amount ) range and Input X(black,other race and male) range then we get,

(b)

   From the above table of value the Least square equation is given by

            Y = 77.5862 + 5.2899 X1+ 17.9367X2 + 16.1718X3

Quantile regression at the 50th percentile is = 50N/100 = N/2 = median

                                             the value N at Black variable = N = 15

                                             and the value of N at other race variable = N = 13

                                            and also the value of N at male variable = N = 62

   So the 50th percentile of Black variable = N/2 = 15/2 = 7.5,

and the 50th percentile of other race variable = N/2 = 13/2 = 6.5,

and also the 50th percentile of male variable = N/2 = 62/2 = 31,

(C)

   and Now we Estimate the model at the 10th, 25th, 75th, and 90th percentiles are given by

           10th percentaile for Black variable = 10N/100 = N/10 = 15/10 = 1.5

            10th percentaile for other race variable = 10N/100 = N/10 = 13/10 = 1.3

and also 10th percentaile for Male variable = 10N/100 = N/10 = 62/10 = 6.2

and also the 25th percentaile for Black variable = 25N/100 = N/4= 15/4 = 3.75

    the 25th percentaile for other race variable = 25N/100 = N/4= 13/4 = 3.25

the 25th percentaile for Male variable = 25N/100 = N/4= 62/4 = 15.5

the 75th percentaile for Black variable = 75N/100 = 75*15/100 = 11.25

and the 75th percentaile for other race variable = 75N/100 = 75*13/100 = 9.75

and also the 75th percentaile for Male variable = 75N/100 = 75*62/100 = 46.5

the 90th percentaile for Black variable = 90N/100 = 9N/10 = 9*15/10 = 4.5

and the 90th percentaile for other race variable = 90N/100 = 9N/10 = 9*13/10 = 11.7

and also the 90th percentaile for Black variable = 90N/100 = 9N/10 = 9*62/10 = 55.8

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SUMMARY OUTPUT Regression Statistics Multiple R 0.189053653 R Square 0.035741284 Adjusted R Square 0.009443319 Standard Error 50.89308955 Observations 114 ANOVA df SS MS F Significance F Regression 3 10560.55862 3520.186 1.359089 0.25914172 Residual 110 284911.7221 2590.107 Total 113 295472.2807 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 77.58616726 7.871516865 9.856571 8.34E-17 61.9866689 93.185666 61.9866689 93.18566562 Black 5.289901969 14.4425821 0.366271 0.714866 -23.331905 33.911709 -23.3319049 33.91170888 other race 17.9367138 15.15025195 1.183922 0.238996 -12.087529 47.960956 -12.0875286 47.96095621 male 16.17179231 9.705931129 1.666176 0.098524 -3.0630844 35.406669 -3.06308444 35.40666907

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