Simple linear regression Show all calculation details Consid

Simple linear regression. Show all calculation details. Consider the data set: (7,11), (10,0), (13,-2).

Compute and interpret the coefficient of correlation.

Compute the least squares line for this data.

mean of x = (7+10+13)/3

= 10

mean of y = (11+0-2)/2

= 3

Variace of (X)= 1/2*[(7-10)^2 +(10-10)^2 + (13-10)^2)

= 9

variance of Y = 1/2*[(11-3)^2 +(0-3)^2 + (-2-3)^2)

= 49

covariance(XY)= 1/2*[(7-10)(11-3) +(10-10)*(0-3) + (13-10)(-2-3))

= -19.5

Correlation (XY) = covariance/ [sd(x) *sd9y)]

= -19.5/3*7

=-0.952857

now equation of regression equation is Y = a +b*x

a = mean(y) - b* mean(x)

b = correlation * sd(y)/ sd(x)

b=-0.952857*7/3

b= -2.16667

a= 3-(-2.16667)*10

thus equation is

Y = 24.66667 - 2.166678 X

= 24.66667