The regional transit authority for a major metropolitan area wants to determine whether there is any relationship between the age of a bus and the annual maintenance cost. A sample of 10 buses resulted in the data in Worksheet 2. Worksheet 2 Age of a Bus (years) Maintenance Cost ($) 1 350 2 370 2 480 2 520 2 590 3 550 4 750 4 800 5 790 5 950 Develop a scatter diagram with the age of a bus as the independent variable. Develop the estimated regression equation that can be used to predict the maintenance cost given the age of a bus. Determine the coefficient of determination, and interpret its meaning in this problem.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
The regional transit authority for a major metropolitan area wants to determine whether there is any relationship between the age of a bus and the annual maintenance cost. A sample of 10 buses resulted in the data in Worksheet 2.
Worksheet 2
| Age of a Bus (years) | Maintenance Cost ($) | |
| 1 | 350 | |
| 2 | 370 | |
| 2 | 480 | |
| 2 | 520 | |
| 2 | 590 | |
| 3 | 550 | |
| 4 | 750 | |
| 4 | 800 | |
| 5 | 790 | |
| 5 | 950 |
Develop a
Develop the estimated regression equation that can be used to predict the maintenance cost given the age of a bus.
Determine the coefficient of determination, and interpret its meaning in this problem.
At the 0.05 level of significance, is there evidence of a linear relationship between the age of a bus and the annual maintenance cost.
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