Textbook Question
"An Unhealthy Commute Use the results of Problem 11 from Section 12.3 to answer the following questions:
a. Predict the mean well-being index composite score of all individuals whose commute time is 20 minutes."
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12. Regression
Prediction Intervals
3:23 minutesProblem 12.4.14a
Textbook Question
"American Black Bears Use the results of Problem 18 from Section 12.3 to answer the following questions:
a. Predict the mean weight of American black bears with a total length of 154.5 cm"
Verified step by step guidance1
Identify the regression equation from Problem 18 in Section 12.3, which relates the total length of American black bears to their weight. This equation is typically in the form \(\\hat{y} = b_0 + b_1 x\), where \(\\hat{y}\) is the predicted mean weight, \(b_0\) is the intercept, \(b_1\) is the slope, and \(x\) is the total length.
Substitute the given total length value, \(x = 154.5\) cm, into the regression equation to find the predicted mean weight.
Calculate the predicted mean weight by performing the arithmetic operations in the regression equation after substitution.
Interpret the result as the estimated average weight of American black bears that have a total length of 154.5 cm based on the regression model.
Optionally, consider the context and any assumptions of the regression model, such as linearity and the range of data used to create the model, to assess the reliability of the prediction.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Linear Regression
Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. In this context, it helps predict the mean weight of bears based on their total length by fitting a line that best describes the data trend.
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Prediction Using Regression Equation
Once a regression equation is established, it can be used to predict the value of the dependent variable for a given independent variable. Here, substituting the bear's length (154.5 cm) into the regression equation yields the predicted mean weight.
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Interpretation of Regression Coefficients
Regression coefficients quantify the relationship between variables: the slope indicates how much the dependent variable changes per unit change in the independent variable, and the intercept represents the expected value when the independent variable is zero. Understanding these helps interpret predictions accurately.
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