The Line of Best Fit

1. The Line of Best Fit Section 2.3

2. definitions • Line of best fit  the line with the smallest value for the sum of the squares of the errors. • Method of Least Squares  the process of finding the line of best fit • Center of Gravity  the coordinates of this point are the mean of the observed x-values and the mean of the observed y-values.

3. Example 1 Y = 7.02x – 3.61 7.02 (82.5) – 3.61 = $2.18 ≈ .0352 In August 1990, Consumer Reports listed the following average prices per pound for four grades of raw hamburger: • regular (72.5% lean), $1.57 • Chuck (80% lean), $1.85 • Round (85% lean), $2.38 • Sirloin (92.5% lean), $2.93 Find the equation of best fit: Verify that the center of gravity is on the line of best fit. Find the sum of the squares of the errors for the line of best fit

4. Next Example… Y = .368x + 3.25 Y = .368 (37.5)+ 3.25 17.05 Y = .368 (17) + 3.25 Y = 9.506 • Refer to the data on wrist and neck size in Example 2. Let x = neck circumference and y=wrist circumference • a. What is the line of best fit for predicting wrist size from neck size? • b. What is the predicted wrist size of a person with a neck circumference of 37.5? • c. What is the predicted wrist size of a person with a neck circumference of 17 in?

5. Homework Pages 101 – 103 1-8, 10