### 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

Phil Ender, 5Jan98