Palisades Eco-Park is a small ecological reserve that admits a relatively small number of visitors on any day, but provides both educational and entertaining lectures, exhibitions, and opportunities to observe nature. The company has collected the following data on labor costs and number of visitors to the park over the last 30 months. Month Labor Cost Visitors 1 $ 25,520 1,400 2 $ 35,869 2,135 3 $ 39,504 2,315 4 $ 31,280 1,830 5 $ 34,405 1,954 6 $ 32,293 1,796 7 $ 31,651 1,816 8 $ 37,889 2,204 9 $ 38,120 2,273 10 $ 46,387 2,941 11 $ 41,667 2,451 12 $ 38,576 2,309 13 $ 34,044 1,989 14 $ 32,788 1,924 15 $ 36,542 2,065 16 $ 26,192 1,729 17 $ 30,307 2,797 18 $ 29,613 2,294 19 $ 27,270 1,986 20 $ 29,654 2,448 21 $ 25,394 1,647 22 $ 24,369 1,478 23 $ 28,556 2,690 24 $ 29,803 3,144 25 $ 27,792 2,135 26 $ 31,322 2,696 27 $ 28,318 2,462 28 $ 29,579 2,512 29 $ 28,108 2,068 30 $ 27,550 1,709 Required: a. Estimate the labor costs assuming 2,200 visitors for the month using the results of a simple regression based on the 30 months of available data. b. What percentage of the variance in the data does the R-squared value explain? c. You learn that starting in month 16, the park started using a different, more automated system for interacting with visitors. Estimate the labor cost assuming 2,200 visitors using the results of a simple regression based on the data for months 16 through 30 only. d. What percentage of the variance in the data does the R-squared value explain?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.3: Modeling Data With Power Functions

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Palisades Eco-Park is a small ecological reserve that admits a relatively small number of visitors on any day, but provides both educational and entertaining lectures, exhibitions, and opportunities to observe nature. The company has collected the following data on labor costs and number of visitors to the park over the last 30 months.

Month	Labor Cost	Visitors
1	$	25,520	1,400
2	$	35,869	2,135
3	$	39,504	2,315
4	$	31,280	1,830
5	$	34,405	1,954
6	$	32,293	1,796
7	$	31,651	1,816
8	$	37,889	2,204
9	$	38,120	2,273
10	$	46,387	2,941
11	$	41,667	2,451
12	$	38,576	2,309
13	$	34,044	1,989
14	$	32,788	1,924
15	$	36,542	2,065
16	$	26,192	1,729
17	$	30,307	2,797
18	$	29,613	2,294
19	$	27,270	1,986
20	$	29,654	2,448
21	$	25,394	1,647
22	$	24,369	1,478
23	$	28,556	2,690
24	$	29,803	3,144
25	$	27,792	2,135
26	$	31,322	2,696
27	$	28,318	2,462
28	$	29,579	2,512
29	$	28,108	2,068
30	$	27,550	1,709

Required:

a. Estimate the labor costs assuming 2,200 visitors for the month using the results of a simple regression based on the 30 months of available data.
b. What percentage of the variance in the data does the R-squared value explain?
c. You learn that starting in month 16, the park started using a different, more automated system for interacting with visitors. Estimate the labor cost assuming 2,200 visitors using the results of a simple regression based on the data for months 16 through 30 only.
d. What percentage of the variance in the data does the R-squared value explain?

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