Question: 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.
Distance to work (miles) Number of Days Absent
1 8
3 5
4 8
6 7
8 6
10 3
12 5
14 2
14 4
18 2
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. What is the 99 percent confidence interval for the regression parameter b1? Based on this interval, what conclusion can you make about the hypotheses that the regression parameter b1 is equal to zero?
d. What is the 99 percent confidence interval for the regression parameter b0? Based on this interval, what conclusion can you make about the hypotheses that the regression parameter b0 is equal to zero?
e. How much of the variation in the sample values of number of days absent does the model you estimated in part b explain?