Question

Obtaining the least squares estimator

Which of the following describes the process for obtaining the least squares estimator?

Select one:

a. Take the first derivative (slope) of the sum of squared errors with respect to the coefficients and set the result to zero.

b. Take the first derivative (slope) of the sum of squared errors with respect to coefficients and minimise the result.

c. Take the first derivative (slope) of the sum of squared errors with respect to the error term and set the result to zero.

d. Take the first derivative (slope) of the sum of squared errors with respect to the error term and minimise the result.

Answer 1

For equation of the objective function of the ordinary least square estimation, we generally set up the regression equation and find the sum of squared errors. In order to find the estimates for OLS, we need to minimise the sum of squared errors. This can be done by taking the partial derivatives of the sum of squared errors and set them equal to zero. This is because minimise or maximize a function means setting the Partial derivatives equal to zero

Select option A.