Question

Sumit wants to find a measure which he can fix the monthly income of persons applying for a job in his department. For a trial project, he collected data on $7$ persons from that department referring to the years of service and monthly income. Find the regression equation $\left(y\right)$ as years of service $\left(x\right)$.

Years of service $\left(x\right)$	11	7	9	5	8	6	10
Income in '00 Rs. $\left(y\right)$	10	8	6	5	9	7	11

• A. $4y=3x+8$
• B. $3y=-4x+8$
• C. $4y=3x+6$
• D. $4y=3x-8$

Answer 1

The correct option is A $4y=3x+8$

$x$	$y$	$xy$	$x^2$	$y^2$
11 7 9 5 8 6 10	10 8 6 5 9 7 11	110 56 54 25 72 42 110	121 49 81 25 64 36 100	100 64 36 25 81 49 121

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

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

$\overline{x}y=\frac{\sum xy}{N}=\frac{469}{7}=67$

$\frac{\sum x^2}{N}=\frac{476}{7}=68$

$\frac{y^2}{N}=\frac{476}{7}=68$

$\frac{\sum y^2}{N}=\frac{976}{7}=68$

${\sigma }_x=\sqrt{\frac{\sum x^2}{N}-(\overline{x}{)}^2}=\sqrt{68-8}=\sqrt{60}$

${\sigma }_y=\sqrt{\frac{\sum y^2}{N}-(\overline{y}{)}^2}=\sqrt{68-8}=\sqrt{60}$

$Cov(x,y)=\overline{xy}-\overline{x}\overline{y}=67-(8\times 8)=3$

$r=\frac{Cov(x,y)}{{\sigma }_x{\sigma }_y}=\frac{3}{60}=\frac{1}{20}\Rightarrow b_{yx}=\frac{Cov(x,y)}{{\sigma }_x^2}=\frac{3}{60}=\frac{1}{20}$

Regression equation will be given by,

$(y-\overline{y})=b_{yx}(x-\overline{x})$

$(y-8)=\frac{1}{20}(x-8)$

so, $x-20y+152=0$