Transforming data for inference
- 1. Focus Fox handout Q’s 3, 6, 7 ,8, 10
- 2. Transforming Data Transformations can straighten a nonlinear pattern. Then, we can use a least-square regression line to make inferences and test a claim about the slope of the population. Pg. 766-767 Transforming data is changing the scale of measurement that was used when data was collected. Linear transformations cannot straighten curved relationship between two variables Functions that are not linear can transform curved relationships to a linear model
- 4. Transforming Data Imagine that you have been put in charge of organizing a fishing tournament in which prizes will be given for the heaviest Atlantic Ocean rockfish caught. You know that many of the fish caught during the tournament will be measured and released. You are also aware that using delicate scales to try to weigh a fish that is flopping around in a moving boat will probably not yield very accurate results. It would be much easier to measure the length of the fish while on the boat. What you need is a way to convert the length of the fish to its weight. You contact the nearby marine research laboratory, and they provide reference data on the length (in centimeters) and weight (in grams) for Atlantic Ocean rockfish of several sizes.
- 5. Transforming Data Because length is one-dimensional and weight (like volume) is three- dimensional, a power model of the form weight = a(length)3 should describe the relationship. What happens if we cube the lengths in the data table and then graph weight versus length3? Pg. 769 Length: 5.2 8.5 11.5 14.3 16.8 19.2 21.3 23.3 25.0 26.7 Weight: 2 8 21 38 69 117 148 190 264 293 Length: 28.2 29.6 30.8 32 33 34 34.9 36.4 37.1 37.7 Weight: 318 371 455 504 518 537 651 719 726 810
- 7. Transforming Data Give the equation of least-squares regression line. Define any variables.
- 8. Transforming Data Suppose a contestant in the fishing tournament catches an Atlantic Ocean rockfish that’s 36 cm long. Use each model to predict the fish’s weight.
- 9. Transforming Data Interpret the value of s in context.