AP Stats Regression Analysis 1 — Questions and Answers
Question 1: What is the purpose of linear regression analysis?
- To model the relationship between a dependent variable and one or more independent variables (Correct answer)
- To prove causation between variables
- To classify data into groups
- To calculate the mode of a dataset
Correct answer: To model the relationship between a dependent variable and one or more independent variables
Linear regression models the linear relationship between variables, enabling prediction and understanding of variable relationships.
Question 2: What does R-squared (R²) measure?
- The proportion of variance in the dependent variable explained by the independent variables (Correct answer)
- The correlation between the independent variables
- The number of outliers in the data
- The sample size needed for significance
Correct answer: The proportion of variance in the dependent variable explained by the independent variables
R² indicates how well the independent variables explain the variability in the dependent variable, ranging from 0 to 1.
Question 3: What is multicollinearity?
- High correlation among independent variables in a regression model (Correct answer)
- A non-linear relationship between variables
- Missing data in the dataset
- Unequal variance across groups
Correct answer: High correlation among independent variables in a regression model
Multicollinearity occurs when independent variables are highly correlated, making it difficult to isolate individual effects.
Question 4: What is the purpose of residual analysis in regression?
- To check whether the assumptions of the regression model are met (Correct answer)
- To calculate the regression coefficients
- To determine the sample size
- To test for correlation only
Correct answer: To check whether the assumptions of the regression model are met
Residual analysis examines the differences between observed and predicted values to validate model assumptions.
Question 5: What assumption must be met for ordinary least squares regression?
- Residuals should be normally distributed with constant variance (Correct answer)
- All variables must be categorical
- The sample size must exceed 1000
- Independent variables must be perfectly correlated
Correct answer: Residuals should be normally distributed with constant variance
OLS regression assumes normality and homoscedasticity of residuals, linearity, and independence of observations.
Question 6: What is the difference between simple and multiple regression?
- Simple regression has one predictor; multiple regression has two or more predictors (Correct answer)
- Simple regression is less accurate
- Multiple regression can only be used with large datasets
- There is no practical difference
Correct answer: Simple regression has one predictor; multiple regression has two or more predictors
Simple regression uses one independent variable while multiple regression includes two or more independent variables.
AP Stats Regression Analysis 1
What is the purpose of linear regression analysis?