13.9 Day 2 Least Squares Regression

Examples of Regression

Example 3 Find the least squares regression line for the points (-3,0), (-1,1), (0,2) and (2,3)

Solution to Example 3 Here is the computation involved in finding the least squares regression line using n= 4 The equation is y = 8/13x + 47/26

Problem 28 Find the Least Squares regression of a line for the given points. Use the regression capabilities of your calculator to verify your results.

We will prove that 1=2 using calculus and the definition of x2: (*) First note that x2 is equal to x*x, that is, x added to itself x times: x*x= x*x x2 = x + x + ... + x (done x times) Take the derivative of each side, on the left using the power rule, and on the right using the sum rule: 2*x = 1 + 1 + ... + 1 (done x times) Now 1 added to itself x times is simply x: 2*x = x Divide each side by x... 2 = 1

Set the partial derivatives = 0 to obtain the values listed Solve for a, the substitute for b By using Solve this equation for b