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 67 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. (a) Is a linear model appropriate to use for these data? Justify your response by referencing the residual plot. Question 2 The computer output from the regression analysis and the boxplot of the residuals are shown. Estimate Error T P Intercept −16.462 9.726 −1.693 0.0953 Distance 0.849 0.049 17.177 0.0000 S=41.025 R-sq=0.819 (b) Identify the intercept of the least-squares regression line and interpret it in the context of the data. Question 3 (c) The researchers plan to calculate a 95 percent confidence interval for the population slope. Identify and check the conditions for the appropriate confidence interval for the population slope.
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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
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 67 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
(a) Is a linear model appropriate to use for these data? Justify your response by referencing the residual plot.
Question 2
The computer output from the regression analysis and the boxplot of the residuals are shown.
| Estimate | Error | T | P | |
| Intercept | −16.462 | 9.726 | −1.693 | 0.0953 |
| Distance | 0.849 | 0.049 | 17.177 | 0.0000 |
| S=41.025 | R-sq=0.819 |
(b) Identify the intercept of the least-squares regression line and interpret it in the context of the data.
Question 3
(c) The researchers plan to calculate a 95 percent confidence interval for the population slope. Identify and check the conditions for the appropriate confidence interval for the population slope.
Question 4
(d) The 95% confidence interval for the population slope was calculated as (0.751,0.947). Based on the confidence interval, do the data provide convincing statistical evidence that foragers with a central home location move faster the farther they are from home? Justify your response.
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The 95% confidence interval for the population slope was calculated as (0.751,0.947). Based on the confidence interval, do the data provide convincing statistical evidence that foragers with a
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