You are a new hire at Laurel Woods Real Estate, which specializes in selling for

Question

You are a new hire at Laurel Woods Real Estate, which specializes in selling foreclosed homes via public auction. Your boss has asked you to use the following data (mortgage balance, monthly payments, payments made before default, and final auction price) on a random sample of recent sales in order to estimate what the actual auction price will be. Add a new variable that describes the potential interaction between the loan amount and the number of payments made Monthly Payments $1,037.10 937.46 752.28 951.89 827.66 983.27 1,075.54 1,087.16 900.01 683.11 915.24 905.67 810.70 891.33 864.38 1,074.73 871.61 1,021.2:3 836.46 1,056.37 Payments Made Loan $ 85,616 111,834 110,890 117,157 97,600 104,400 113,800 116,400 100,000 92,800 105,206 105,900 94,700 105,600 104,106 85,700 113,600 119,400 90,600 104,500 Auction Price $17,625 56,775 46,275 16,600 40,700 63,100 72,600 72,300 58,100 37,100 52,600 51,900 43,200 52,600 42,700 22,200 77,000 69,000 35,600 63,000 38 18 12 36 34 38 25 20 30 24 58

Explanation / Answer

Using R software we can have the answers,

CODE:

loan <-c(85616,11834,110890,117157,97600,104400,113800,116400,100000,92800,105200,105900,94700,105600,104100,85700,113600,119400,90600,104500)
MonthlyPay <- c(1037.1,937.46,752.28,951.89,827.66,983.27,1075.54,1087.16,900.01,683.11,915.24,905.67,810.70,891.33,864.38,1074.73,871.61,1021.23,836.46,1056.37)
PayMade <- c(1,38,6,3,18,12,22,35,33,36,34,38,25,20,7,30,24,58,3,22)
AucPrice <- c(17625,56775,46275,16600,40700,63100,72600,72300,58100,37100,52600,51900,43200,53600,42700,22200,77000,69000,35600,63000)
reg <- lm(AucPrice~loan+MonthlyPay+PayMade+loan*PayMade)
summary(reg)

OUTPUT:

> loan <- c(85616,11834,110890,117157,97600,104400,113800,116400,100000,92800,105200,105900,94700,105600,104100,85700,113600,119400,90600,104500)

> MonthlyPay <- c(1037.1,937.46,752.28,951.89,827.66,983.27,1075.54,1087.16,900.01,683.11,915.24,905.67,810.70,891.33,864.38,1074.73,871.61,1021.23,836.46,1056.37)

> PayMade <- c(1,38,6,3,18,12,22,35,33,36,34,38,25,20,7,30,24,58,3,22)

> AucPrice <- c(17625,56775,46275,16600,40700,63100,72600,72300,58100,37100,52600,51900,43200,53600,42700,22200,77000,69000,35600,63000)

> reg <- lm(AucPrice~loan+MonthlyPay+PayMade+loan*PayMade)

> summary(reg)

Call:

lm(formula = AucPrice ~ loan + MonthlyPay + PayMade + loan *

PayMade)

Residuals:

Min 1Q Median 3Q Max

-32767 -5467 2734 8659 23223

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -6.637e+04 7.024e+04 -0.945 0.360

loan 7.857e-01 5.830e-01 1.348 0.198

MonthlyPay 2.374e+01 3.332e+01 0.713 0.487

PayMade 2.371e+03 1.659e+03 1.429 0.174

loan:PayMade -1.713e-02 1.588e-02 -1.078 0.298

Residual standard error: 16000 on 15 degrees of freedom

Multiple R-squared: 0.3684, Adjusted R-squared: 0.2

F-statistic: 2.187 on 4 and 15 DF, p-value: 0.1199

The equation is,

Auction Price = -66370 + 0.786 * Loan + 23.74 * Monthly Payment + 2371 * Payment Made - 0.017 * 1X3

t value for the interaction term is -1.08.

Now for the interaction effect, the acceptance region is, (-12.7062, 12.7062).

So, the t value belongs to the acceptance region. So, we can accept the null hypothesis that there is no effect of the interaction.

So, This is not significant, so we can conclude there is no effect of the interaction effect for estimation of the Auction Price.

Predictor Coefficient SE Coefficient t p- value Constant -66370 70240 -0.945 0.360 Loan 0.786 0.583 1.348 0.198 Monthly Payment 23.74 33.32 0.713 0.487 Payments Made 2371 1659 1.429 0.174 (Loan)(Payments Made) -0.017 0.016 -1.078 0.298

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