Question

36. Continuing Problem 18, suppose that the antique collector believes that the rate of increase of the auction price with the age of the item will be driven upward by a large number of bidders. How would you revise the multiple regression equation developed previously to model this feature of the problem? a. Estimate your revised equation using the data in the file P10_18.xlsx. b. Interpret each of the estimated coefficients in your revised model. c. Does this revised model fit the given data better than the original multiple regression model? Explain why or why not.

Auction Auction Price Age of Item Number Bidders 1 $946 113 9 2 $1,336 126 10 3 $744 115 7 4 $1,979 182 11 5 $1,522 150 9 6 $1,235 127 13 7 $1,483 159 9 8 $1,152 117 13 9 $1,545 175 8 10 $1,262 168 7 11 $845 127 7 12 $1,055 108 14 13 $1,253 132 10 14 $1,297 137 9 15 $1,147 137 8 16 $1,080 115 12 17 $1,550 182 8 18 $1,047 156 6 19 $1,792 179 9 20 $729 108 6 21 $854 143 6 22 $1,593 187 8 23 $1,175 111 15 24 $1,713 137 15 25 $1,356 194 5 26 $1,822 156 12 27 $1,884 162 11 28 $1,024 117 11 29 $2,131 170 14 30 $785 111 7 31 $1,092 153 6 32 $2,041 184 10

Answer 1

36. Continuing Problem 18, suppose that the antique collector believes that the rate of increase of the auction price with the age of the item will be driven upward by a large number of bidders. How would you revise the multiple regression equation developed previously to model this feature of the problem?

a. Estimate your revised equation using the data in the file P10_18.xlsx.

The estimated regression line is

Auction Price = -1,336.7221+12.7362* Age of Item +85.8151* Number Bidders

b. Interpret each of the estimated coefficients in your revised model.

When age of item increases by 1 unit, auction price increases by 12.7362.

When Number Bidders increases by 1 , auction price increases by 85.8151.

c. Does this revised model fit the given data better than the original multiple regression model? Explain why or why not.

R square =0.893.

89.3% of variance in auction price is explained by the model.

( compare this with your previous model and interpret)

Excel Addon Megastat used.

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

Regression Analysis
	R²	0.893
	Adjusted R²	0.885	n	32
	R	0.945	k	2
	Std. Error	133.137	Dep. Var.	Auction Price
ANOVA table
Source	SS	df	MS	F	p-value
Regression	4,277,159.7034	2	2,138,579.8517	120.65	8.77E-15
Residual	514,034.5153	29	17,725.3281
Total	4,791,194.2188	31
Regression output					confidence interval
variables	coefficients	std. error	t (df=29)	p-value	95% lower	95% upper
Intercept	-1,336.7221	173.3561	-7.711	1.67E-08	-1,691.2751	-982.1690
Age of Item	12.7362	0.9024	14.114	1.60E-14	10.8906	14.5818
Number Bidders	85.8151	8.7058	9.857	9.14E-11	68.0099	103.6204