In the Multiple Regression Model with Two Regressors,the Formula for the Slope

question 29

Essay

In the multiple regression model with two regressors,the formula for the slope of the first explanatory variable is (small letters refer to deviations from means as in ).
An alternative way to derive the OLS estimator is given through the following three step procedure.
Step 1: regress Y on a constant and ,and calculate the residual (Res1).
Step 2: regress on a constant and ,and calculate the residual (Res2).
Step 3: regress Res1 on a constant and Res2.
Prove that the slope of the regression in Step 3 is identical to the above formula.

---

Definitions:

Straight-Line Depreciation

A technique for distributing the expense of a physical asset evenly over its lifespan on an annual basis.

Sewing Machines

Mechanical or electromechanical devices used to stitch fabric and other materials together with thread.

Hourly Wages

Compensation paid to employees based on the number of hours worked, often set at a fixed rate per hour.

Sewing Machine Operators

Sewing machine operators are skilled workers who operate sewing machines to join, reinforce, decorate, or perform related sewing operations in the manufacturing of garment or non-garment products.