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.  Use the estimated regression equation developed in part (c) to develop a 95% confidence interval for the expected number of days absent for employees living 5 miles from the company (to 1 decimal). Least squares equation from part c:
Days Absent = 7.269 + -0.194 Distance

Distance to Work	Number of Days Absent
1	9
4	6
4	9
6	8
8	7
10	4
12	7
14	3
14	6
18	3

Answer 1

Let Y=Number of Days Absent

X=Distance to Work

The model that we want to estimate is

We calculate the following

n=10 is the sample size

The sample means are

The sum of squares are

The estimated value of the slope is

The estimated value of intercept is

The estimated regression line is

that is the answer in part c should be

(Note: This is different from what has been pasted, but for the data given, the above is correct )

Now the rest

The sum of square errors is

The mean square Error is

The standard error of regression is

the estimated number of days absent for employees living miles () from the company is

The standard error of for   is

The level of significance for 95% confidence interval is

the right tail critical value is obtained using

The degrees of freedom for t is n-2=10-2=8

Using the t tables for df=8 and area under the right tail=0.025 (combined area under both tails=0.05), we get

Now the 95% confidence interval

ans: a 95% confidence interval for the expected number of days absent for employees living 5 miles from the company is [6.2,8.9]