Question

8. Is the regression line the best fitting line that minimizes the squared deviations from the observed value to the predicted value? Explain your answer.

Answer 1

Ans:

In general, when we use to predict the actual response y_i we make a prediction error (or residual error) of size:

A line that fits the data "best" will be one for which the n prediction errors i.e. one for each observed data point, are as small as possible in some overall sense,so to achieve this we minimize the sum of the squared prediction errors.

We need to find the values b₀ and b₁ that make the sum of the squared prediction errors the smallest it can be i.e. to minimize