At first glance, a linear model appears to represent the data best as there seems to be a positive correlation between the weights and lengths of the alligators; as the length increases, the weight also tends to increase. However, to determine the best fit model, one would typically analyze the data visually through a scatter plot and evaluate the correlation coefficient as well as residuals. Additionally, calculating and comparing the goodness-of-fit measures, such as R-squared values, for both linear and possibly non-linear models (like exponential or polynomial) would provide more insight. Given the nature of biological data, which can often exhibit non-linear relationships, a polynomial regression might better capture the variation in the data. Ultimately, a statistical analysis would confirm the model that minimizes error and provides higher predictive accuracy.
In order to keep track of the local alligator population, individual alligators are often tagged. This enables researchers to collect data on each animal continuously. The current weights and lengths of 13 alligators are given in the table.
Weight (lbs.) Length (in.)
51 74
44 61
80 86
28 58
70 88
110 94
83 86
61 72
54 74
106 90
90 86
33 63
95 95
Based on patterns in the data, at first glance, which model appears to represent this data best? Why?
Which model is actually the best fit for the data? How do you know?
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