# A collector of antique grandfather clocks believes that the price

A   collector of antique grandfather clocks believes that the price (in dollars)   received for the clocks at an antique auction increases with the age of the   clocks and with the number of bidders.  Thus the model is   hypothesized is where Y = auction price, x1 = age of clock (years) and x2 =   number of bidders.      A sample of 32 auction prices   of grandfather clocks, along with their ages and the number of bidders, is   given below.        a) State the multiple   regression equation.        b)   Interpret the meaning of the slopes b1 and b2 in the model.         c)   Interpret the meaning of the regression coefficient b0.         d) Test   H0: β2 = 0 against H1: β2 > 0.  Interpret your finding.         e) Use a   95% confidence interval to estimate β2.  Interpret the p-value   corresponding to the estimate β2.  Does the confidence interval   support your interpretation in d)?         f)   Determine the coefficient of multiple determination r2Y.12 and interpret its   meaning.         g) Perform   a residual analysis on your results and determine the adequacy of the fit of   the model.         i) At α ± =   0.05, is there evidence of positive autocorrelation in the residuals?          j) Suppose   the collector, having observed many auctions, believes that the rate of   increase of the auction price with age will be driven upward by a large   number of bidders.  In other words, the collector believes that the   age of clock and the number of bidders should interact.  Is there   evidence to support his claim that the rate of change in the mean price of   the clocks with age increases as the number of bidders   increases?  Should the interaction term (x1 x2) be included in the   model?  If so, what is the multiple regression equation?

Age (x1) Bidders (x2) Price (y)   127 13 1235   115 12 1080   127 7 845   150 9 1522   156 6 1047   182 11 1979   156 12 1822   132 10 1253   137 9 1297   113 9 946   137 15 1713   117 11 1024   137 8 1147   153 6 1092   117 13 1152   126 10 1336   170 14 2131   182 8 1550   162 11 1884   184 10 2041   143 6 854   159 9 1483   108 14 1055   175 8 1545   108 6 729   179 9 1792   111 15 1175   187 8 1593   111 7 785   115 7 744   194 5 1356   168 7 1262

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