Question 3.

The data give the selling price at auction of 32 antique grandfather clocks. Also recorded is

the age of the clock and the number of people who made a bid. Here are the description of

the variables. Variable

Age (x1) Bidders (x2) Price (y)

Description Age of the clock (years) Number of individuals participating in the bidding Selling price (pounds sterling)

An interaction model is used and the following output are obtained from minitab:

Regression Analysis : Price versus Age , Bidders , AgeBidders The regression equation is

Price = 323 + 0.87

Age 93.4 Bidders + 1.30 AgeBidders

Predictor Constant Age Bidders AgeBidders

S = 88.3674

Coef 322.8 0.873

93.41 1.2979

RSq

SE Coef 293.3 2.020 29.71 0.2110

= 95.4%

T P 1.10 0.281 0.43 0.669 3.14 0.004 6.15 0.000

RSq(adj) = 94.9%

MS F P 1524183 195.19 0.000

7809

Analysis of Variance Source DF SS Regression 3 4572548 Residual Error 28 218646 Total 31 4791194

(a) Write down a multiple regression model with interaction term using Price as response and the others as predictors.

3

(b) Test if 1 is significantly different from 0.

(c) Based on previous result, can you say that Age is not significantly correlated to Price? Why?

(d) Test if the interaction term is significant.

(e) Interpret the result in previous question.

(f) Construct a 90% confidence interval for the regression coefficient for Bidders.

(g) Test the global utility of the model.

(h) Write down a potentially better model for this data (use the results of previous ques- tions!).