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Mathematics, 09.05.2021 02:40 brighamc23

The movement patterns of animals are believed to be affected by their physiological states (such as hunger), predation risk, and other factors such as whether they are searching for food for their young. Optimal foraging theory predicts that foragers (animals searching for food) with a central home location should move faster the farther they are from home. American beavers are foragers with a central home location that make foraging trips from their lodge and then return. To test the optimal foraging theory, researchers trapped and radio-tagged a random sample of American beavers from the population in a certain region and recorded their movements over the course of about a year. The researchers fit a least-squares regression line to the data, where the explanatory variable was distance to lodge, in meters, and the response variable was speed, in meters per hour. The resulting residual plot of the regression analysis is shown. alt_text alt_text alt_text Identify the intercept of the least-squares regression line and interpret it in the context of the data.

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