For 10 observations on price (x) and supply(y), the following data was obtained `sum x=130` `sum y=220` `sum x^2 =2288` `sum y^2=5506` and `sum xy=3467` what is the line of regression of y on x

Options

A. `y=0.91x+0.74`
B. `y=1.02x+8.74`
C. `y=1.02x-7.02`
D. `y=0.91x-7.02`

Answer

B

Explanation

Line of regression of y on x is :
`y-bary=b_(yx)(x-barx)`
`bary=(Sigmay)/(n),barx=(Sigmax)/(n)rArr bary=(220)/(100)=22,barx=(130)/(10)=13`
`b_(yx)=r.(sigma_(y))/(sigma_(x))`
`r=(n Sigmaxy-(Sigmax)(Sigmay))/(sqrt([nSigmax^(2)-(Sigmax)^(2)][nSigmay^(2)-(Sigmay)^(2)]))`
`=(10(3467)-(130)(220))/(sqrt([(10xx2288)-130^(2)][(10xx5506)-(220^(2))]))`
`r=0.962`
`sigma_(y)=sqrt((Sigmay^(2))/(n)-((Sigmay)/(n))^(2)) rArr sigma_(y)=8.2, sigma_(x)=7.73.`
`rArr b_(yx)=0.962xx(8.2)/(7.73)=1.02`
`rArr" Line of regression of y on x is :"`
`y-22=1.02(x-13)`
`rArr y=1.02x+8.74`