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

Years of service | 11 | 7 | 9 | 5 | 8 | 6 | 10 |

Income (Rs. In 1000’s) | 10 | 8 | 6 | 5 | 9 | 7 | 11 |

(a) What is the degree of association (correlation) between years of service and income?

(b) Find the regression equation of income on years of service.

(c) What initial start would you recommend for a person applying for the job having served in a similar capacity in another company for 13 years?

Ans

Years of service | Income (Rs. In 1000’s) | [X-8] dx | dx | [Y-8] dy | dy | dxdy |

11 | 10 | +3 | 9 | +2 | 4 | +6 |

7 | 8 | -1 | 1 | 0 | 0 | 0 |

9 | 6 | +1 | 1 | -2 | 4 | -2 |

5 | 5 | -3 | 9 | -3 | 9 | +9 |

8 | 9 | 0 | 0 | +1 | 1 | 0 |

6 | 7 | -2 | 4 | -1 | 1 | +2 |

10 | 11 | +2 | 4 | +3 | 9 | +6 |

56 | 56 |
| 28 |
| 28 | 21 |

**(a) What is the degree of association (correlation) between years of service and income?**

Ans

Conclusion: There is a high degree of correlation between year of service and income.

**(b) Find the regression equation of income on years of service.**

Ans

Regression equation of income (Y) on years of service (X): –

Y = a=bx |

Regression equation of income on years of service

Years of service (X) | Income (Y) | X | XY |

11 | 10 | 121 | 110 |

7 | 8 | 49 | 56 |

9 | 6 | 81 | 54 |

5 | 5 | 25 | 25 |

8 | 9 | 64 | 72 |

6 | 7 | 36 | 42 |

10 | 11 | 100 | 110 |

56 | 56 | 476 | 469 |

**(c) What initial start would you suggest for a person applying for the job having served in a similar capacity in another company for 13 years?**

Ans

When x = 13 years, the average income would be

y =2 + 0.75x

= 2 + 0.75(13)

= Rs 11,750

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