A park has kept the number of visitors since its opening in January. For the first six months of the year, the following numbers were recorded: Month Number of visitors Month Number of visitors January 133 April 640 February 183 May 1,879 March 285 June 2,550 Estimate the intercept and slope of the linear regression equation for forecasting the numbers of visitors. What are the forecasts for July through December of the year using the regression equation?
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.
A park has kept the number of visitors since its opening in January. For the first six months of the year, the following numbers were recorded:
|
Month |
Number of visitors |
Month |
Number of visitors |
|
January |
133 |
April |
640 |
|
February |
183 |
May |
1,879 |
|
March |
285 |
June |
2,550 |
- Estimate the intercept and slope of the linear regression equation for forecasting the numbers of visitors. What are the forecasts for July through December of the year using the regression equation?
- The numbers of visitors to the park were 2,150 in July, and 2,660. Use Holt’s method with α=0.15 and β= 0.10 to find the one-step-ahead and two-step-ahead forecasts for September and October, respectively.
As per guidelines, we will only answer first question.
Use the given data to form excel table:
| X | Y | X*Y | X*X | |
| 1 | 133 | 133 | 1 | |
| 2 | 183 | 366 | 4 | |
| 3 | 285 | 855 | 9 | |
| 4 | 640 | 2560 | 16 | |
| 5 | 1879 | 9395 | 25 | |
| 6 | 2550 | 15300 | 36 | |
| Sum | 21 | 5670 | 28609 | 91 |
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