Least Square Regression Line

Least Square Regression:

In general, when we use ŷ<_ii = b₀ + b_ix_i to predict the actual response y_i, we make a prediction error of size:

e_i = y_i – ŷ_i

A line that fits the data ‘best’ will be one for which prediction errors – one for each observed data point. That is as small as possible in some overall sense. One way to achieve this goal is to invoke the least squares criterion which says to minimize the sum of the squared prediction errors. That is:

i. The equation of the best fitting line is ŷ<_ii = b₀ + b_ix_i

ii. We just need to find the values b₀ that make the sum of the squared prediction errors the smallest it can be.

iii. That is we need to find the values b₀ and b₁ that minimize.