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 9
3 6
4 9
6 8
8 7
10 2
12 4
14 3
14 5
18 1

Required:
a. Develop the least squares estimated regression equation used to predict the number of days absent given a certain distance to work.
b. Is there a significant relationship between the two variables? Use α = 0.05.
c. Did the estimated regression equation provide a good fit? Explain.
d. Is the estimated regression equation appropriate and adequate?
e. Are there any outliers in the data? If yes, identify them.

y = -0.43841X + 9.34565

Step-by-step explanation:

Given the data:

Distance to work (x) :

1

3

4

6

8

10

12

14

14

18

Y:

9

6

9

8

7

2

4

3

5

1

The least square estimated regression equtyol obtained using  a linear regression calculator is :

y = -0.43841X + 9.34565

Yes, from the correlation Coefficient value, R which yields - 0.8444, shows they a strong linear relationship exists between the two variables.

The obtained regression equation is appropriate

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet