Reconsider the data in Exercise 3.12. Define a new set of transformed variables as the first difference of the original variablesRegress through the origin. Compare the estimate of the slope from this first-difference approach with the estimate obtained from the iterative method in Exercise 3.12.
Exercise 3.12The data in Table E3.6 give the monthly sales for a cosmetics manufacturer (y1) and the corresponding monthly sales for the entire industry (x1). The units of both variables are millions of dollars.
TABLE E3.6 Cosmetic Sales Data
t
xt
yt
1
5.00
0.318
10
6.16
0.650
2
5.06
0.330
11
6.22
0.655
3
5.12
0.356
12
6.31
0.713
4
5.10
0.334
13
6.38
0.724
5
5.35
0.386
14
6.54
0.775
6
5.57
0.455
15
6.68
0.78
7
5.61
0.460
16
6.73
0.796
8
5.80
0.527
17
6.89
0.859
9
6.04
0.598
18
6.97
0.88
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