Question 1. We have data that give the selling price at auction of 32 antique gr

Question

Question 1. We have data that 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 ids the description of the variables. Variable Age (1) Age of the clock (years) Bidders (z2) Number of individuals participating in the bidding Price (y) Selling price (pounds sterling) Description (a). Write down a first order multiple regression model using Price as response and the Age and number of bidders as predictors. The first order model was fit to the data, leading to the following Minitab regression output. Regression Analysis: Price versus Age, Bidders, AgeBidders Predictor Constant Coef SE Coef -1339.0 173.8 7.70 0.000 12.7406 0.9047 14.08 0.000 AGE(X1) NUMBIDS(X2) 85.953 8.729 9.85 0.000 S= 133.485 R-Sq-89.2% R-Sq (adj )-88.5% Analysis of Variance DF MS Source Regression Residual Error 29 516727 17818 Total 2 4283063 2141531 XXXX XXXX 31 4799790

Explanation / Answer

(a) Regression equation is -

Price = -1339 + 12.7406 * X1 + 85.953* X2

Where X1 = age

and X2 = Number of bidders

(g) Utility of the model would be tested F -value given in the ANOVA table-

We have F-value = 2141531 / 17818 = 120.189

So p-value is given by P( F2 , 29 > 120.189 ) = 0

This value is less than .05 and thus we reject the null hypothesis and conclude that model is significant.

(h) Price estimate when X1 = 130 and X2 = 8

= -1339 + 12.7406 * 130 + 85.953 * 8

=1004.9

TY!

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