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.

Loan			Monthly Payments			Payments Made		Auction Price
$	85,611		$	999.83		1		$	74,700
	114,848			932.18		37			51,150
	111,456			747.28		3			44,700
	113,240			1,076.05		4			16,600
	97,600			836.53		22			40,700
	104,400			983.27		23			63,100
	113,800			1,075.54		17			72,600
	116,400			1,087.16		35			72,300
	100,000			900.01		33			58,100
	92,800			683.11		36			37,100
	105,200			915.24		34			52,600
	105,900			905.67		38			51,900
	94,700			810.70		25			43,200
	105,600			891.33		20			52,600
	104,100			864.38		7			42,700
	85,700			1,074.73		30			22,200
	113,600			871.61		24			77,000
	119,400			1,021.23		58			69,000
	90,600			836.46		3			35,600
	104,500			1,056.37		22			63,000

Determine the regression equation. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

Auction Price= _________ + _________ Loan+ _________ Monthly Payment+ ________ Payments made+ ________ x1x3

Complete the following table. (Round your answers to 3 decimal places. Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by a minus sign.)

Predictor	Coefficient	SE Coefficient	t	p-value
Constant
Loan
Monthly Payment
Payments Made
(Loan)(Payments Made)

Compute the t-value corresponding to the interaction term. (Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

t-value= _______

Do a test of the null hypothesis to check if the interaction is significant. (Use the 0.05 significance level.)

This is ______ (significant/not significant), so we conclude that there is ______ (interaction/no interaction)

Answer 1

using excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.602431
R Square	0.362923
Adjusted R Square	0.193036
Standard Error	15319.42
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	4	2.01E+09	5.01E+08	2.13626	0.126534
Residual	15	3.52E+09	2.35E+08
Total	19	5.53E+09
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	86512.04	66886.37	1.293418	0.215431	-56052.9	229077
Loan	-0.43619	0.577048	-0.7559	0.461418	-1.66614	0.79376
Monthly Payments	8.739849	32.15727	0.271785	0.789493	-59.8018	77.28145
Payments Made	-4343.14	2184.129	-1.9885	0.06532	-8998.5	312.2189
loan*payment mades	0.042172	0.0203	2.0774	0.055356	-0.0011	0.08544

the regression equation is

Auction Price= 86512.04 -0.436* Loan+8.740* Monthly Payment-4343.14*Payments made+ 0.042* x1x3

Predictor	Coefficient	SE Coefficient	t	p-value
Constant	86512.04	66886.37	1.293418	0.215431
Loan	-0.43619	0.577048	-0.7559	0.461418
Monthly Payment	8.739849	32.15727	0.271785	0.789493
Payments Made	-4343.14	2184.129	-1.9885	0.06532
(Loan)(Payments Made)	0.042172	0.0203	2.0774	0.055356

Compute the t-value corresponding to the interaction term

t-value= 2.08

Do a test of the null hypothesis to check if the interaction is significant. (Use the 0.05 significance level.)

This is not significant , so we conclude that there is no interaction