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The Manager of a Company Wants to Find a Measure Which He Can Use to Fix the Monthly Wages of Persons Applying for a Job in the Production Department. as an Experimental Project, He Collected Data O - HSC Commerce (Marketing and Salesmanship) 12th Board Exam - Mathematics and Statistics

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Question

The manager of a company wants to find a measure which he can use to fix the monthly wages of persons applying for a job in the production department. As an experimental project, he collected data of 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 (` in thousands) 10 8 6 5 9 7 11

Find regression equation of income on the years of service. 

Solution

For the given data we have the following table 

Year of service income xy `X^2` `Y^2`
11 10 110 121 100
7 8 56 49 64
9 6 54 81 36
5 5 25 25 25
8 9 72 64 81
6 7 42 36 49
10 11 110 100 121
56 56 469 476 496

Here `n =7,∑x=56,∑y=56,∑xy=469,∑x^2=476,∑y^2=496` 

Now  `barx=∑x/n=56/7=8` 

`bary=∑y/n=56/7=8`  

The regression of y on x is given by 

`b_yx=(n∑_xy-∑x∑y)/(n∑x^2-(∑x)^2)` 

=`(7xx469-56xx56)/(7xx476-(56)^2)` 

=`(3283-3136)/(3332-3136)` 

=`147/196=0.75` 

Hence the regression line of y on x is given by 

`y-bary=b_(yx)(x-barx)` 

`y-8=0.75(x-8)`

`y-8=0.75x-6.00`

`y=0.75x+2`

 or `y=3/4x+2`

⇒ `4y=3x+8`

  Is there an error in this question or solution?

APPEARS IN

 2017-2018 (March) (with solutions)
Question 6.1.2 | 3.00 marks
Solution The Manager of a Company Wants to Find a Measure Which He Can Use to Fix the Monthly Wages of Persons Applying for a Job in the Production Department. as an Experimental Project, He Collected Data O Concept: Sequencing in Management Mathematics.
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