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 $ 26,420 2,300 2 $ 37,134 3,507 3 $ 40,897 3,803 4 $ 32,383 3,006 5 $ 35,618 3,211 6 $ 33,432 2,951 7 $ 32,767 2,983 8 $ 39,225 3,621 9 $ 39,464 3,735 10 $ 48,023 4,832 11 $ 43,137 4,026 12 $ 39,937 3,794 13 $ 35,244 3,268 14 $ 33,944 3,161 15 $ 37,831 3,393 16 $ 27,116 2,840 17 $ 31,376 4,595 18 $ 30,657 3,769 19 $ 28,232 3,263 20 $ 30,700 4,022 21 $ 26,289 2,705 22 $ 25,228 2,428 23 $ 29,563 4,420 24 $ 30,854 5,165 25 $ 28,773 3,507 26 $ 32,426 4,429 27 $ 29,317 4,044 28 $ 30,622 4,126 29 $ 29,099 3,398 30 $ 28,522 2,808
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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 | $ | 26,420 | 2,300 |
| 2 | $ | 37,134 | 3,507 |
| 3 | $ | 40,897 | 3,803 |
| 4 | $ | 32,383 | 3,006 |
| 5 | $ | 35,618 | 3,211 |
| 6 | $ | 33,432 | 2,951 |
| 7 | $ | 32,767 | 2,983 |
| 8 | $ | 39,225 | 3,621 |
| 9 | $ | 39,464 | 3,735 |
| 10 | $ | 48,023 | 4,832 |
| 11 | $ | 43,137 | 4,026 |
| 12 | $ | 39,937 | 3,794 |
| 13 | $ | 35,244 | 3,268 |
| 14 | $ | 33,944 | 3,161 |
| 15 | $ | 37,831 | 3,393 |
| 16 | $ | 27,116 | 2,840 |
| 17 | $ | 31,376 | 4,595 |
| 18 | $ | 30,657 | 3,769 |
| 19 | $ | 28,232 | 3,263 |
| 20 | $ | 30,700 | 4,022 |
| 21 | $ | 26,289 | 2,705 |
| 22 | $ | 25,228 | 2,428 |
| 23 | $ | 29,563 | 4,420 |
| 24 | $ | 30,854 | 5,165 |
| 25 | $ | 28,773 | 3,507 |
| 26 | $ | 32,426 | 4,429 |
| 27 | $ | 29,317 | 4,044 |
| 28 | $ | 30,622 | 4,126 |
| 29 | $ | 29,099 | 3,398 |
| 30 | $ | 28,522 | 2,808 |
Required:
a. Estimate the labor costs assuming 3,100 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 3,100 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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