Question

A data set consists of the following data points:

(3,5), (5,8), (6,13)

The slope of the best fit line is 2.5. Find the y-intercept of this line.

Answer 1

There are standard formulae for the parameters of the regression line.
One version is as follows.
Assume y=mx+b, with n data points.
m(slope) = (sum(x^2)sum(y)-sum(x)sum(xy))/(nsum(x^2)-(sum(x)^2)
b (intercept)=(n*sum(xy)-(sum(x))(sum(y)))/(nsum(x^2)-(sum(x)^2)
where sum(...) = summation over the data points.
Using the given data, check that m=2.5, and subsequently calculate b.

These formulae can be derived from first principles based on least squares and using basic calculus.