Question

Derive the ordinary least squares estimator in case of multiple regression analysis

Answer 1

The ordinary least squares (OLS) estimator for the simple linear regression case, only one independent variable (only one x), was derived. The procedure relied on combining calculus and algebra to minimize of the sum of squared deviations.

The simple linear case although useful in illustrating the OLS procedure is not very realistic. Rarely, are you interested in only one independent variable’s potential affect on the dependent variable, y.

For example, if interested forecasting sales for your would you find only own price in the econometric forecasting equation(s). Other factors such as competitors’ price and the general state of the economy will affect your sales.

This more realistic case, more than one independent variable, is the subject of this reading assignment. The OLS estimator is derived for the multiple regression case. Multiple regression simply refers to the inclusion of more than one independent variable.