# Exercise 3.1

1. The HRD manager of a company wants to find a measure which he can use to fix the monthly income of persons applying for the job in the production department. As an experimental project, he collected data of 7 persons from that department referring to years ofservice and their monthly incomes.

 Years of service (X) 11 7 9 5 8 6 10 Monthly Income (Rs.1000’s) (Y) 10 8 6 5 9 7 11

(i) Find the regression equation of income on years of service.
(ii) What initial start would you recommend for a person applying for the job after having served in similar capacity in another company for 13 years?

## Solution

2. Calculate the regression equations of X on Y and Y on X from the following data:

 X 10 12 13 17 18 Y 5 6 7 9 13

## Solution

3. For a certain bivariate data on 5 pairs of observations given∑ x = 20,      ∑ y = 20,     ∑ x^2 = 90,       ∑ y^2 = 90,       ∑ xy = 76
To Calculate:  (i) cov( x, y)       (ii) b_yx  and b_xy,          (iii) r

## Solution

4. From the following data estimate y when x = 125

 X 120 115 120 125 126 123 Y 13 15 14 13 12 14

## Solution

5. The following table gives the aptitude test scores and productivity indices of 10 workers selected at random.

 Aptitude score (X) 60 62 65 70 72 48 53 73 65 82 Productivity Index (Y) 68 60 62 80 85 40 52 62 60 81

Obtain the two regression equations and estimate:
(i) The productivity index of a worker whose test score is 95.
(ii) The test score when productivity index is 75.

## Solution

6. Compute the appropriate regression equation for the following data:

 X  [Independent Veriable] 2 4 5 6 8 11 Y [Dependent Veriable] 18 12 10 8 7 5

## Solution

7. The following are the marks obtained by the students in Economics (X) and Mathematics (Y)

 X 59 60 61 62 63 Y 78 82 82 79 81

Find the regression equation of Y on X.

## Solution

8. For the following bivariate data obtain the equations of two regression lines:

 X 1 2 3 4 5 Y 5 7 9 11 13

## Solution

9. From the following data obtain the equation of two regression lines:

 X 6 2 10 4 8 Y 9 11 5 8 7

## Solution

10. For the following data, find the regression line of Y on X

 X 1 2 3 Y 2 1 6

Hence find the most likely value of y when x = 4.

## Solution

11. From the following data, find the regression equation of Y on X and estimate Y when X = 10.

 X 1 2 3 4 5 6 Y 2 4 7 6 5 6

## Solution

12. The following sample gives the number of hours of study (X) per day for an examination and marks (Y) obtained by 12 students.

 X 3 3 3 4 4 5 5 5 6 6 7 8 Y 45 60 55 60 75 70 80 75 90 80 75 85

Obtain the line of regression of marks on hours of study.