Question

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

Years of service	11	7	9	5	8	6	10
Income (Rs in thousands)	10	8	6	5	9	7	11

Find regression equation of income on the years of service.

Answer 1

We formulate the table from the given data

Table

$\overline{x}=\frac{\sum x}{n}=\frac{56}{7}=8$

$\overline{y}=\frac{\sum y}{n}=\frac{56}{7}=8$

$byx=\frac{\sum xy-\frac{1}{n}\sum x\sum y}{\sum x^2-\frac{1}{n}{(\sum x)}^2}$

$=\frac{469-\frac{1}{7}.56.56}{476-\frac{1}{7}{\left(56\right)}^2}$

$=\frac{147}{196}=0.75$

$\therefore$Regression line of y on x

$y-\overline{y}=byx(x-\overline{x})$

$y-8=\frac{3}{4}(x-8)$

$4y-32=3x-24$

Or $4y=3x+8$