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 ______, so we conclude that there is _________

Answer 1

Answer:

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

Auction Price = 86,512.043 + (-0.436 ) Loan + (8.740 ) Monthly Payment + (-4,343.142 ) Payments Made +(0.042 ) 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	86,512.043	66,886.373	1.293	0.215
Loan	-0.436	0.577	-0.756	0.461
Monthly Payment	8.740	32.157	0.272	0.790
Payments Made	-4,343.142	2,184.129	-1.989	0.065
(Loan)(Payments Made)	0.042	0.020	2.077	0.055

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 = 2.077

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 effect.

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis

Regression Analysis
	R²	0.363
	Adjusted R²	0.193	n	20
	R	0.602	k	4
	Std. Error of Estimate	15319.416	Dep. Var.	Auction Price
Regression output						confidence interval
variables		coefficients	std. error	t (df=15)	p-value	95% lower	95% upper
Intercept	a =	86,512.043	66,886.373	1.293	.2154	-56,052.886	229,076.971
x1	b1 =	-0.436	0.577	-0.756	.4614	-1.666	0.794
x2	b2 =	8.740	32.157	0.272	.7895	-59.802	77.281
x3	b3 =	-4,343.142	2,184.129	-1.989	.0653	-8,998.502	312.219
x1x3	b4 =	0.042	0.020	2.077	.0554	-0.001	0.085
ANOVA table
Source	SS	df	MS	F	p-value
Regression	2,005,388,553.307	4	501,347,138.327	2.14	.1265
Residual	3,520,267,821.693	15	234,684,521.446
Total	5,525,656,375.000	19