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Ch. 10 - Correlation and Regression
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 10 - Correlation and RegressionProblem 10.4.19
Chapter 10, Problem 10.4.19

Dummy Variable Refer to Data Set 18 “Bear Measurements” in Appendix B and use the sex, age, and weight of the bears. For sex, let 0 represent female and let 1 represent male. Letting the response variable represent weight, use the variable of age and the dummy variable of sex to find the multiple regression equation. Use the equation to find the predicted weight of a bear with the characteristics given below. Does sex appear to have much of an effect on the weight of a bear?


Female bear that is 20 years of age
Male bear that is 20 years of age

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Step 1: Understand the problem. This is a multiple regression problem where the response variable is the weight of the bear, and the predictor variables are age (a continuous variable) and sex (a categorical variable represented as a dummy variable: 0 for female, 1 for male). The goal is to find the regression equation and use it to predict the weight of a bear based on its age and sex.
Step 2: Set up the multiple regression equation. The general form of a multiple regression equation is: y=b+b1x1+b2x2, where y is the response variable (weight), b is the intercept, b1 and b2 are the coefficients for the predictor variables age (x1) and sex (x2), respectively.
Step 3: Use statistical software or a calculator to compute the regression coefficients. Input the data for age, sex, and weight into the software. The software will calculate the values of b, b1, and b2 using the least squares method. These coefficients will form the regression equation.
Step 4: Use the regression equation to predict the weight of a bear. For a female bear (sex = 0) that is 20 years old, substitute x1 = 20 and x2 = 0 into the regression equation. For a male bear (sex = 1) that is 20 years old, substitute x1 = 20 and x2 = 1 into the regression equation.
Step 5: Analyze the effect of sex on weight. Examine the coefficient b2 in the regression equation. If this coefficient is significantly different from 0 (based on its p-value), it indicates that sex has a statistically significant effect on the weight of a bear. Compare the predicted weights for the male and female bears to see the practical impact of sex on weight.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Dummy Variables

Dummy variables are numerical variables used in regression analysis to represent categorical data. They take on values of 0 or 1 to indicate the absence or presence of a particular category. In this case, sex is represented as 0 for female and 1 for male, allowing the regression model to include categorical information in a quantitative analysis.
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Multiple Regression

Multiple regression is a statistical technique that models the relationship between one dependent variable and two or more independent variables. It helps in understanding how the independent variables, such as age and sex in this case, influence the dependent variable, which is the weight of the bears. The resulting equation can be used to predict the weight based on the given characteristics.
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Interpreting Regression Coefficients

Interpreting regression coefficients involves understanding the impact of each independent variable on the dependent variable. In this context, the coefficients associated with age and the dummy variable for sex will indicate how much weight is expected to change with a one-unit increase in age or a change in sex from female to male. This analysis helps determine if sex significantly affects bear weight.
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