Linear Statistical Models: Regression

A Derivation

Consider the following graph:

At the point where the curve is the lowest, the slope of the line tangent to the curve has a slope of zero. Calculus is used to find the point where the function is a minimum, i.e., where the slope of the tangent line is zero.

Deriving the Least Squares Regression Coefficients:

The Regression Equation

Computational Simplification

From Calculus...

• By differential calculus...
• Find the derivative; set it to 0; solve for the unknown variable.
• First time, differentiate with respect to a.

Derivation of the Constant

More Calculus...

• Next differentiate with respect to b.
• Find the derivative; set it to 0; solve for the unknown variable.

Deriving the Regression Coefficient

In Deviation Score Form

Linear Statistical Models Course