A local government conducted a study to investigate the relationship between the number of unauthorized days employees are absent per year and the distance(miles) between home and work for employees. The table below gives the results for ten employees. Distance to work (miles) Number Days Absent 1 8 3 5 4 8 6 7 8 6 10 3 12 5 14 2 14 4 18 2 Sketch a scatter diagram for the data. Is a linear relationship reasonable? Explain. Develop the least squares estimate regression equation that relates the distance to work to the number of days absent. Predict the number of days absent for an employee that lives 5 miles from work.
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 local government conducted a study to investigate the relationship between the number of unauthorized days employees are absent per year and the distance(miles) between home and work for employees.
The table below gives the results for ten employees.
Distance to work (miles) Number Days Absent
| 1 | 8 |
| 3 | 5 |
| 4 | 8 |
| 6 | 7 |
| 8 | 6 |
| 10 | 3 |
| 12 | 5 |
| 14 | 2 |
| 14 | 4 |
| 18 | 2 |
-
Sketch a
scatter diagram for the data. Is a linear relationship reasonable? Explain. -
Develop the least squares estimate regression equation that relates the distance to work to
the number of days absent.
-
Predict the number of days absent for an employee that lives 5 miles from work.
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