Question

XYZ company plans to advertise some vacancies. The Manager is asked to suggest the monthly salary for these vacancies based on the years of experience. To do so, the Manager studies the years of service and the monthly salary drawn by the existing employees in the company.

Following is the data that the Manager refers to:

Years of service (X)	11	7	9	5	8	6	10
Monthly salary (in ₹ 1000)(Y)	10	8	6	5	9	7	11

1. Find the regression equation of monthly salary on the years of service.
2. If a person with 13 years of experience applies for a job in this company, what monthly salary will be suggested by the Manager?

Answer 1

a. Number of observations = n = 7.

Here, the line of regression from Y to X is required.

X	Y	XY	X2
11	10	110	121
7	8	56	49
9	6	54	81
5	5	25	25
8	9	72	64
6	7	42	36
10	11	110	100
Total	56	469	476

`barX = (sumX)/n`

= `56/7`

= 8

`barY = (sumY)/n`

= `56/7`

= 8

`b_(YX) = (sumXY - 1/n sumXsumY)/(sumX^2 - 1/n(sumX)^2)`

= `(469 - (56 xx 56)/7)/(476 - (56)^2/7)`

= `(469 - 448)/(476 - 448)`

= `21/28`

= `3/4`

The line of regression of Y on X is given as

`(y - barY) = b_(YX)(x - barX)`

`Y - 8 = 3/4(X - 8)`

`\implies` 4Y – 32 = 3X – 24

`\implies` 4Y – 3X – 8 = 0

b. If X = 13

Then, 4Y – 3 × 13 – 8 = 0

`\implies` 4Y – 39 – 8 = 0

`\implies` 4Y – 47 = 0

`\implies` 4Y = 47

Y = 11.75

Then, monthly salary is ₹ 11,750.