A collector of antique grandfather clocks sold at auction believes that the price received for the clocks depends on both the age of the clocks and the number of bidders at the auction. Thus, he hypothesizes the first-order model y = b0 + b1 x1 + b2 x2 + e where y = Auction price 1dollars2 x1 = Age of clock 1years2 x2 = Number of bidders A sample of 32 auction prices of grandfather clocks, along with their age and the number of bidders, is given in Table 12.1.

a. Use scatterplots to plot the sample data. Interpret the plots.

b. Use the method of least squares to estimate the unknown parameters b0, b1, and b2 of the model.

c. Find the value of SSE that is minimized by the least squares method.

d. Estimate s, the standard deviation of the model, and interpret the result.

Auction Price Data Age x1 Number of Bidders x2 Auction Price y Age x1 Number of Bidders x2 Auction Price y 127 13 $1,235 170 14 $2,131 115 12 1,080 182 8 1,550 127 7 845 162 11 1,884 150 9 1,522 184 10 2,041 156 6 1,047 143 6 845 182 11 1,979 159 9 1,483 156 12 1,822 108 14 1,055 132 10 1,253 175 8 1,545 137 9 1,297 108 6 729 113 9 946 179 9 1,792 137 15 1,713 111 15 1,175 117 11 1,024 187 8 1,593 137 8 1,147 111 7 785 153 6 1,092 115 7 744 117 13 1,152 194 5 1,356 126 10 1,336 168 7 1,262