AP Statistics Section 4.1 A Transforming to Achieve Linearity

1. AP Statistics Section 4.1 ATransforming to Achieve Linearity

2. In Chapter 3, we learned how to analyze relationships between two quantitative variables that showed a linear pattern. When two-variable data shows a nonlinear relationship, we must develop new techniques for finding an appropriate model.

3. The process of changing the data mathematically to find a linear model is called ___________ or ____________ the data. transforming re-expressing

4. The transformations we will study are __________ and ______ transformations. These transformations change the scale of measurement that was used when the data was collected. power logarithmic

5. Example 1: Consider the average length and weight at different ages for Atlantic rockfish.

6. Use your calculator to draw a scatterplot of the data for length (x), in L1 and weight (y), in L2. Is it linear? ____ Is there a pattern? _____ Since there is a pattern, let’s try to “straighten” thedata. no yes

7. Since length is __ dimensional and weight (which depends on volume) is __ dimensional, let’s graph length3 (x), in L3 vs. weight (y) in L2. Is the scatterplot linear? ____ yes Highlight L3 ENTER L1 ^ 3 ENTER

8. Calculate the LSL on the transformed points (length3, weight) and determine r2.

9. Predict the weight of an Atlantic Rockfish that is 31.5cm long.

10. Now we’ll look at the residual plot.