Month Rental Returns Car Wash Costs 2,380 $10,825 $11,865 $11,332 $12,422 $13,850 $14,419 $14,935 $15,738 $13,563 January.... February 2,421 March. . 2,586 2,725 April. May 2,968 June.. 3,281 July August. September. October..... 3,353 3,489 3,057 2,876 2,735 $11,889 $12,683 $13,796 November... December. 2,983
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.
Least-Squares Regression
Bargain Rental Car offers rental cars in an off-airport location near a major tourist destination in California. Management would like to better understand the variable and fixed portions of it car washing costs. The company operates its own car wash facility in which each rental car that is returned is thoroughly cleaned before being released for rental to another customer. Management believes that the variable portion of its car washing costs relates to the number of rental returns. Accordingly, the following data have been compiled:
Required:
1. Prepare a scattergraph plot. (Place car wash costs on the vertical axis and rental returns on the horizontal axis.)
2. Using least-squares regression, estimate the variable cost per rental return and the monthly fixed cost incurred to wash cars. The total fixed cost should be estimated to the nearest dollar and the variable cost per rental return to the nearest cent.
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