# 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 ( | 11 | 7 | 9 | 5 | 8 | 6 | 10 |

Monthly Income (Rs.1000’s) ( | 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?

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 |

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

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

| 120 | 115 | 120 | 125 | 126 | 123 |

| 13 | 15 | 14 | 13 | 12 | 14 |

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

Aptitude score ( | 60 | 62 | 65 | 70 | 72 | 48 | 53 | 73 | 65 | 82 |

Productivity Index ( | 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.

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

| 2 | 4 | 5 | 6 | 8 | 11 |

| 18 | 12 | 10 | 8 | 7 | 5 |

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

| 59 | 60 | 61 | 62 | 63 |

| 78 | 82 | 82 | 79 | 81 |

Find the regression equation of Y on X.

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

| 1 | 2 | 3 | 4 | 5 |

| 5 | 7 | 9 | 11 | 13 |

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

| 6 | 2 | 10 | 4 | 8 |

| 9 | 11 | 5 | 8 | 7 |

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

| 1 | 2 | 3 |

| 2 | 1 | 6 |

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

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

| 1 | 2 | 3 | 4 | 5 | 6 |

| 2 | 4 | 7 | 6 | 5 | 6 |

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

| 3 | 3 | 3 | 4 | 4 | 5 | 5 | 5 | 6 | 6 | 7 | 8 |

| 45 | 60 | 55 | 60 | 75 | 70 | 80 | 75 | 90 | 80 | 75 | 85 |

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