Question

We have a dataset with n= 10 pairs of observations (Li, Yi), and n n r; = 683, y = 813, n n n { x = 47,405, tiyi = 56,089, y = 66, 731. i=1 i=1 i=1 What is the line of best fit for this data?

Answer 1

The general equation for the simple linear regression line is given as below:

ŷ = a + bx

Where the formula for the coefficients a and b are given as below:

Slope = b = (∑XY – n*Xbar*Ybar)/(∑X^2 – n*Xbar^2)

y-intercept = a = Ybar – b*Xbar

From given information, we have

n = 10

∑x = 683

∑y = 813

∑x^2 = 47405

∑y^2 = 66731

∑xy = 56089

Xbar = ∑x/n = 683/10 = 68.3

Ybar = ∑y/n = 813/10 = 81.3

b = (∑XY – n*Xbar*Ybar)/(∑X^2 – n*Xbar^2)

b = (56089 - 10*68.3*81.3)/( 47405 - 10*68.3^2)

b = 0.742098

a = Ybar – b*Xbar

a = 81.3 - 0.742098*68.3

a = 30.61471

ŷ = a + bx

So, the required equation for regression line is given as below:

ŷ = 30.61471 + 0.742098x