Abigail Faith is the CEO of AFB Company, a purveyor of computer-aided design software. Abigail has instructed her distributor that her software should be licensed to industrial customers at annual fees, F, which should depend principally on two factors - the number of designers, D, and the number of work stations, W, at each company, according to the following relation:
F = X DY WZ, where X = 1000, Y = .55, and Z = .15
While Abigail allows her distributors some latitude in pricing in order to "get the sale," she's concerned that her instructions may not have been taken seriously. Based on the following data (random sample of 50 clients), the question is whether there is evidence that Abigail's guidelines are not being observed.
Client
Designers
(D) Work Stations (W) Annual Fee (F)
1 50 10 $12,146
2 394 172 $21,030
3 535 288 $21,659
4 236 13 $14,951
5 266 264 $32,021
6 363 148 $23,086
7 244 17 $25,228
8 182 116 $18,575
9 543 525 $38,066
10 87 72 $9,042
11 891 51 $20,010
12 561 499 $52,978
13 978 790 $40,364
14 821 469 $45,340
15 675 582 $61,629
16 863 779 $30,522
17 612 456 $48,157
18 884 275 $36,763
19 75 35 $10,422
20 517 76 $15,125
21 192 173 $11,836
22 324 29 $23,531
23 55 52 $7,798
24 787 111 $27,471
25 148 107 $11,321
26 737 221 $25,090
27 491 209 $42,666
28 654 519 $25,107
29 572 534 $29,566
30 229 86 $18,692
31 355 249 $13,875
32 135 73 $20,253
33 989 47 $44,927
34 248 121 $15,217
35 595 450 $18,958
36 762 547 $60,994
37 282 210 $14,531
38 411 190 $69,682
39 574 556 $17,217
40 377 348 $35,763
41 688 56 $34,403
42 806 431 $70,869
43 363 260 $17,457
44 160 64 $8,240
45 414 357 $40,521
46 351 345 $14,173
47 961 730 $77,115
48 782 748 $46,472
49 612 320 $77,188
50 159 62 $12,090
(The data can be copied and pasted into Excel or SPSS)
The first thing one needs to do is to take the logarithm of both sides (either log base 10 ["log"] or log base e ["ln" - called "natural log"]). This will result in a linear (multiple regression) model, with variables (logF, logD, logW) or (LnF, LnD, LnW). All hypothesis tests should use α = .05.
a) Test whether there is evidence that Abigail's distributors are violating her edict that X = 1000.
b) Test whether there is evidence that Abigail's distributors are violating her edict that Y = .55.
c) Test whether there is evidence that Abigail's distributors are violating her edict that Z = .15.
d) What is your summary conclusion after the 3 above analyses?
e) Test (jointly) whether there is evidence that Abigail's distributors are violating her edict.