We appreciate your visit to To find out whether violent crime rates differ by region a researcher has regressed the violent crime rate measured in acts per 100 000 residents. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To interpret the regression coefficient for the 'West' dummy variable in the context of this study, we need to understand how dummy variables and coefficients work in multiple regression.
In a regression analysis where the dependent variable is the violent crime rate (measured in acts per 100,000 residents) and the independent variables include regional dummy variables, each coefficient for a dummy variable represents the change in the dependent variable when that dummy is 1, compared to the baseline or reference category, usually omitted from the model.
What does the coefficient mean?
- The coefficient for the 'West' dummy variable (-97.86) indicates that the violent crime rate in the West is 97.86 acts per 100,000 residents lower than the reference region.
Which answer choice is correct?
- Given the explanation above, option c is correct: "The violent crime rate in the West is 97.86 acts per 100,000 residents lower than the national average."
- This interpretation assumes that the baseline or reference category in the regression includes averages from other regions, making the national average a suitable benchmark for comparison.
Learn about Regression Coefficients and Dummy Variables:
- Dummy Variables: These are binary variables (0 or 1) used in regression models to represent categorical data, like "region" in this case.
- Coefficient Interpretation: The regression coefficient indicates how much the dependent variable (violent crime rate) is expected to change when the independent variable (here, being in the West region) changes, holding all other factors constant.
Why is it important to compare to a baseline?
- In most regressions, dummy variables are compared to a baseline category, which helps establish a point of reference. This allows for clear interpretation of how being in one region (like the West) affects the dependent variable relative to that baseline.
Understanding these basic concepts will help you properly interpret multiple regression outputs like the one in your question.
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