Question

A new online auction site specializes in selling automotive parts for classic cars. The founder of the company believes that the price received for a particular item increases with its age (i.e., the age of the car on which the item can be used in years) and with the number of bidders. The Excel multiple regression output is shown below.

Summary measures
Multiple R			0.8391
R-Square			0.7041
Adj R-Square			0.6783
StErr of Estimate			148.828
ANOVA Table
Source	df	SS	MS	F
Explained	2	1212039.4	606019.7	27.3601
Unexplained	23	509444.9	22149.8
Regression coefficients
	Coefficient	Std Err	t-value	p-value
Constant	-1242.99	331.204	-3.7529	0.0010
Age of Item	75.017	10.65	7.0459	0.0000
Number of Bidders	13.973	10.44	1.3380	0.1940

(A) Estimate a multiple regression model for the data.

(B) Which of the variables in this model have regression coefficients that are statistically different from 0 at the 5% significance level?

Given your findings in (B), which variables, if any, would you choose to remove from the model estimated in (A)? Explain your decision.

Answer 1

a) From the coefficient column of the bottom most table, the multiple regression model here could be obtained as:

Price = Constant + Age of Item * Coefficient for Age of Item + Number of Bidders * Coefficient for number of bidders

Price = -1242.99 + 75.017*Age + 13.973*Number of bidders.

b) A parameter is statistically significant if the p-value for the variable is less than the level of significance. Here we are given the level of significance as 0.05.

We see that the constant term and the coefficient for Age of Item, the p-values are less than 0.05 and therefore the 2 variables are significant but for Number of bidders the p-value is greater than 0.05, and therefore the variable is not significant in the model. Therefore the coefficients of Age of Item and constant are significantly different from 0 in the model.

Given our findings in the previous part, we see that the Number of bidders variable is not signficantly different from 0 and therefore we will choose that to remove from the model estimated in (A)