Conceptual Question on Least Squares Estimation Method

1. Which condition must be satisfied in case of least square method?
2. Why is the least square method the best?
3. What does the least-squares method minimize?
4. How do you calculate least squares estimate?

Which condition must be satisfied in case of least square method?

The method of least squares assumes that the best fit curve of a given type is the curve that has the minimal sum of deviations, i.e., least square error from a given set of data.

Why is the least square method the best?

An analyst using the least squares method will generate a line of best fit that explains the potential relationship between independent and dependent variables. The least squares method provides the overall rationale for the placement of the line of best fit among the data points being studied.

What does the least-squares method minimize?

The method of least squares actually defines the solution for the minimization of the sum of squares of deviations or the errors in the result of each equation. Find the formula for sum of squares of errors, which help to find the variation in observed data. The least-squares method is often applied in data fitting.

How do you calculate least squares estimate?

It is calculated using ^σe= ⎷1T−k−1T∑t=1e2t,(5.3) (5.3) σ ^ e = 1 T − k − 1 ∑ t = 1 T e t 2 , where k is the number of predictors in the model. Notice that we divide by T−k−1 T − k − 1 because we have estimated k+1 parameters (the intercept and a coefficient for each predictor variable) in computing the residuals.