STAT 420
Examples for 10/09/2007 (2)
Fall 2007
A collector of antique grandfather clocks knows that the price received for the clocks
increases linearly with the age of the clocks. Moreover, the collector hypothesizes that
the auction price of the clocks will increase linearly as the number of bidders increases.
Thus, the following first-order model is hypothesized:
Y =
β
0
+
β
1
x
1
+
β
2
x
2
+
ε
where
Y = Auction price (dollars)
x
1
= Age of clock (years)
x
2
= Number of bidders
A sample of 32 auction prices of grandfather clocks, along with their age and the number
of bidders, is given in the table below.
Age,
x
1
Number of
Bidders,
x
2
Auction
Price, Y
Age,
x
1
Number of
Bidders,
x
2
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