Problem $3$: Absent

A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance $($miles$)$ between home and work for the employees. A sample of $10$ employees was chosen, and the following data were collected.

a$.$ Develop a scatter chart for these data. Does a linear relationship appear reasonable? Explain.

b$.$ Use the data to develop an estimated regression equation that could be used to predict the number of days absent given the distance to work. What is the estimated regression model?

c$.$ How much of the variation in the sample values of number of days absent does the model you estimated in part $($b$)$ explain?