ovides 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 $ 25,820 1,700 2 $ 36,290 2,592 3 $ 39,968 2,811 4 $ 31,648 2,222 5 $ 34,809 2,373 6 $ 32,672 2,181 7 $ 32,023 2,205 8 $ 38,334 2,676 9 $ 38,568 2,760 10 $ 46,933 3,572 11 $ 42,157 2,976 12 $ 39,030 2,804 13 $ 34,444 2,415 14 $ 33,173 2,336 15 $ 36,971 2,508 16 $ 26,500 2,099 17 $ 30,663 3,397 18 $ 29,961 2,786 19 $ 27,590 2,412 20 $ 30,003 2,972 21 $ 25,692 2,000 22 $ 24,655 1,794 23 $ 28,892 3,267 24 $ 30,153 3,817 25 $ 28,119 2,592 26 $ 31,690 3,274 27 $ 28,651 2,989 28 $ 29,927 3,050 29 $ 28,438 2,511 30 $ 27,874 2,075 Required: a. Estimate the labor costs assuming 2,500 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 2,500 visitors using the results of a simple regression based on the data for months 16 through 30 only.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Please answer C. and D.
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 | $ | 25,820 | 1,700 |
| 2 | $ | 36,290 | 2,592 |
| 3 | $ | 39,968 | 2,811 |
| 4 | $ | 31,648 | 2,222 |
| 5 | $ | 34,809 | 2,373 |
| 6 | $ | 32,672 | 2,181 |
| 7 | $ | 32,023 | 2,205 |
| 8 | $ | 38,334 | 2,676 |
| 9 | $ | 38,568 | 2,760 |
| 10 | $ | 46,933 | 3,572 |
| 11 | $ | 42,157 | 2,976 |
| 12 | $ | 39,030 | 2,804 |
| 13 | $ | 34,444 | 2,415 |
| 14 | $ | 33,173 | 2,336 |
| 15 | $ | 36,971 | 2,508 |
| 16 | $ | 26,500 | 2,099 |
| 17 | $ | 30,663 | 3,397 |
| 18 | $ | 29,961 | 2,786 |
| 19 | $ | 27,590 | 2,412 |
| 20 | $ | 30,003 | 2,972 |
| 21 | $ | 25,692 | 2,000 |
| 22 | $ | 24,655 | 1,794 |
| 23 | $ | 28,892 | 3,267 |
| 24 | $ | 30,153 | 3,817 |
| 25 | $ | 28,119 | 2,592 |
| 26 | $ | 31,690 | 3,274 |
| 27 | $ | 28,651 | 2,989 |
| 28 | $ | 29,927 | 3,050 |
| 29 | $ | 28,438 | 2,511 |
| 30 | $ | 27,874 | 2,075 |
Required:
a. Estimate the labor costs assuming 2,500 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 2,500 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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