Unformatted text preview: AP-Stats Test #3 – Re-expressing data & creating a mathematical model How do they figure out the weight of alligators? Biologists who track animals need to gather accurate data for a variety of parameters, including weight. The scientists who study alligators do not like to weigh the alligators. This tends to be quite dangerous. Instead, they measure the length of the alligator (this can be measured from a safe distance). Some very brave junior level biologists have done some measurements of length and weight for a few alligators; the data are presented in the table. Create an appropriate model for estimating the weight of an alligator from its length. Use your model to estimate the weight of an alligator that is 105 inches long. Make sketches of graphs, and explain your reasoning. Solution: Graphing Weight vs. Length results in a curved scatterplot.. The curve looks exponential (or power?). To straighten it, let’s try log(Weight) vs. Length. This looks linear. But we need to check the residuals. Here is the same graph with the Least Squares Regression Line (LSRL).
Length (inches) 58 61 69 74 78 88 90 94 114 128 147 Weight (pounds) 28 40 36 54 57 70 102 124 197 366 640 Here is the residual plot. It shows random scatter, so this LSRL is an appropriate model. The equation for the LSRL is: log(Weight ) = 0.5921 + 0.01518 Length . For an alligator with Length 105 inches, we get log(Weight ) = 0.5921 + 0.01518(105) log(Weight ) = 2.1857 Weight = 10 2.1857 = 153.3 The model predicts that an alligator measuring 105 inches in length will have a weight of about 153 pounds. (This seems reasonable when one looks at the data.) (It would be incorrect to state that the weight will be 153 pounds.) ...
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- Regression Analysis, LSRL, 153 pounds, 105 inches