1. AP STATISTICS Section 4.1 Transforming to Achieve Linearity

2. Objective: To be able to use least squares regression line techniques to develop a model for non-linear data. Goals: 1. When working with non-linear data we want to apply a function to one or both variables in order to “straighten” the data. 2. Next, we will use LSRL techniques to develop a model for the “transformed” data. 3. Last, use the inverse function to develop a model for the original relationship.

6. Ex. Create a model for the NCAA March Madness Tournament that plots the number of teams versus the round of the tournament. Data set:

8. A good indicator that a power model may be better than an exponential is that the x values cover a large range of values. Ex. Planetary data. Use a planet’s average distance from the sun to create a model to predict it’s year. A.U.: 0.39, 0.72, 1.00, 1.52, 5.20, 9.54, 19.19, 30.06, 39.53 Year: 0.24, 0.61, 1.00, 1.88, 11.86, 29.46, 84.07, 164.82, 247.68

9. Work:

10. Ex. Use the number of days alive to predict the body weight of Mr. Reid’s dog. Days: 1, 51, 64, 85, 118 Weight: 0.625, 9.900, 12.750, 19.000, 35.700