Question

A company wants to study the relationship between an employee's length of employment and their
number of workdays absent. The company collected the following information on a random sample of
seven employees.

Number of workdays absent 4,2,3 , 5, ,7 ,7 8
length of employment(in yrs) 10, 5, 9 , 2 , 2 ,2 0

1. in this problem whuch is the dependent variable, what is the correlation? and interpret its meaning.

what is the coefficient of determination? interpret its meaning

2. suposse you know that a person has worked for the company for 8 years. how many workdays would you predict he/ she would be absent?

3. Interpret in physical terms the meaning of slope in this example

Answer 1

(1)

(i) Dependent Variable: Number of workdays absent

(ii)

From the given data, the following Table is calculated:

X	Y	XY	X2	Y2
4	10	40	16	100
2	5	10	4	25
3	9	27	9	81
5	2	10	25	4
7	2	14	49	4
7	2	14	49	4
8	0	0	64	0
Total = 36	30	115	216	218

So,

Correlation is:

- 0.7479

Interpretation:

There is slightly strong inverse relationship between x and y.

(iii) Coefficient of determination is given by:

R² = (-0.7479)² = 0.5594

Interpretation:

55.94 % is the percentage of the variance in the dependent variable that is predictable from the independent variable.

(2)

So,

the Regression Line is:

For x = 8, we get:

                                                =1 (Round to integer)

So,

Answer is:

1

(3)

Slope = -1.273 means that for every increase of 1 year of experience, umber of workdays absence will reduce by 1.273 days.