AP Statistics Linear Regression Quiz

What is the purpose of least squares regression in statistics?

• To find the line of best fit that minimizes the sum of the squared residuals between the predicted values and the actual values of a dependent variable based on one or more independent variables.

• To find the line of best fit that minimizes the sum of the absolute residuals between the predicted values and the actual values of a dependent variable based on one or more independent variables.

• To find the line of best fit that maximizes the sum of the squared residuals between the predicted values and the actual values of a dependent variable based on one or more independent variables.

• To find the line of worst fit that maximizes the sum of the squared residuals between the predicted values and the actual values of a dependent variable based on one or more independent variables.

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Explain the concept of residuals in linear regression.

• Residuals in linear regression are the differences between the observed values and the predicted values.

• Residuals are the predicted values in linear regression

• Residuals are the sum of the observed and predicted values in linear regression

• Residuals are the standard deviation of the observed values in linear regression

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How are residual plots used to assess the validity of a linear regression model?

• Residual plots are used to visualize the independent variables in a linear regression model.

• Residual plots are used to calculate the p-value of a linear regression model.

• Residual plots are used to determine the correlation coefficient of a linear regression model.

• Residual plots are used to examine the patterns and distribution of residuals in order to assess the validity of a linear regression model.

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What does the slope coefficient represent in a linear regression equation?

• The slope coefficient represents the correlation between the explanatory and response variables.

• The slope coefficient represents the average value of the explanatory variable.

• The slope coefficient represents the standard deviation of the explanatory variable.

• The slope coefficient represents the change in the explanatory variable for a one-unit change in the response variable.

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What does the intercept coefficient represent in a linear regression equation?

• The intercept coefficient represents the value of the independent variable when all dependent variables are equal to zero.

• The intercept coefficient represents the value of the dependent variable when all independent variables are equal to zero.

• The intercept coefficient represents the maximum value of the dependent variable across all observations.

• The intercept coefficient represents the average value of the dependent variable across all observations.

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Define influential observations in the context of linear regression.

• Data points that have a positive impact on the regression model.

• Data points that have a minor impact on the regression model.

• Data points that have a significant impact on the regression model.

• Data points that have no impact on the regression model.

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What are the assumptions of linear regression?

• Linearity, Independence, Heteroscedasticity, Normality, No multicollinearity

• Linearity, Independence, Homoscedasticity, Normality, No multicollinearity

• Non-linearity, Dependence, Homoscedasticity, Normality, Multicollinearity

• Linearity, Dependence, Homoscedasticity, Normality, No multicollinearity

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How can multicollinearity affect the interpretation of regression coefficients?

• Multicollinearity can lead to biased estimates of regression coefficients.

• Multicollinearity can make regression coefficients unstable and difficult to interpret.

• Multicollinearity can improve the accuracy of regression coefficients.

• Multicollinearity has no effect on the interpretation of regression coefficients.

Explain the concept of heteroscedasticity in linear regression.

• Heteroscedasticity refers to the presence of outliers in linear regression.

• Heteroscedasticity refers to the equal variability of the error term in linear regression.

• Heteroscedasticity refers to the unequal variability of the error term in linear regression.

• Heteroscedasticity refers to the correlation between the independent variables in linear regression.

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What are some techniques to deal with outliers in linear regression?

• Using linear regression without any modifications

• Ignoring the outliers and proceeding with the analysis

• Some techniques to deal with outliers in linear regression are: Removing the outliers from the dataset, Transforming the data using techniques like log transformation, Using robust regression techniques like RANSAC or Theil-Sen regression, Using regularization techniques like L1 or L2 regularization.

• Adding more outliers to balance the dataset