Question

An art collector is studying the relationship between the selling price of a painting and two independent variables. The two independent variables are the number of bidders at the particular auction and the age of the painting, in years. A sample of 25 paintings revealed the following sample information.

Painting		Auction Price		Bidders		Age		Painting		Auction Price		Bidders		Age
1		3,470		10		67		14		4,020		6		79
2		3,500		8		56		15		4,190		4		83
3		3,700		7		73		16		4,130		3		71
4		3,860		4		71		17		4,130		9		89
5		3,920		12		99		18		4,370		5		103
6		3,900		10		87		19		4,450		3		106
7		3,830		11		78		20		4,390		8		93
8		3,940		8		83		21		4,380		8		88
9		3,880		13		90		22		4,540		4		96
10		3,940		13		98		23		4,660		5		94
11		4,200		0		91		24		4,710		3		88
12		4,060		7		93		25		4,880		1		84
13		4,200		2		97

Develop a multiple regression equation using the independent variables number of bidders and age of painting to estimate the dependent variable auction price. (Round your answers to 2 decimal places.)

A. Price = __________ + _______________ bidders +_______________ age.

B. Complete the following table: (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

(it is 4 columns: the "t" column is small)

	Predictor Coefficient SE Coefficient t p-value Constant Bidders Age

Discuss the equation. Does it surprise you that there is an inverse relationship between the number of bidders and the price of the painting? (Round your answers to 1 decimal place.)

C. The price decreases by __________as each additional bidder participates.

D. Meanwhile the price increases by ______________ as the painting gets older.

E. While one would expect OLDER or NEWER (choose) to be worth more, it is unexpected t hat the price goes UP or DOWN (choose) as LESS or MORE (choose) bidders participate.

. Create an interaction variable and include it in the regression equation. (Negative answers should be indicated by a minus sign. Round your answers to 2 decimal places.)

F. Price = _____________ + ______________ Bidders + ___________________ Age + ________________ x1x2.

G. Complete the following table: (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.)

	Predictor Coefficient SE Coefficient t p-value Constant Bidders Age

x1x2 ____ ______ ___ ____ (this line goes under Age with chart

What is the corresponding t value to the interaction term? (Round your answer to 2 decimal places.)

H. The t-value corresponding to the interaction term is_____________. This is SIGNIFICANT or NOT SIGNIFICANT (choose), so we conclude there in INTERACTION or NO INTERACTION (choose). The interaction should BE INCLUDED or NOT BE INCLUDED (choose) in the regression equation.

Answer 1