AP Statistics Linear Regression

Define 'linear regression'.

• A statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation.

• A technique used to predict future values based on historical data without considering relationships.

• A method for analyzing categorical data to find patterns and trends.

• A process of transforming non-linear data into a linear format for easier analysis.

What does the slope of a linear regression indicate in the context of caffeine intake and study time?

• For each additional 1 mg of caffeine, the study time is predicted to increase by 0.164 hours.

• For each additional 1 mg of caffeine, the study time is predicted to decrease by 0.164 hours.

• The slope indicates no relationship between caffeine intake and study time.

• The slope indicates that study time is independent of caffeine intake.

What does a correlation coefficient of r = -1 indicate?

• A perfect positive linear relationship between two variables.

• No linear relationship between two variables.

• A perfect negative linear relationship between two variables.

• A weak negative linear relationship between two variables.

What does a random residual plot indicate?

• It suggests that a linear model is appropriate for the data.

• It indicates that the data has a non-linear relationship.

• It shows that the model is overfitting the data.

• It implies that there are outliers in the dataset.

What does it mean if the correlation coefficient is close to 0?

• It indicates a strong positive linear relationship between the two variables.

• It indicates a weak or no linear relationship between the two variables.

• It indicates a strong negative linear relationship between the two variables.

• It indicates a perfect linear relationship between the two variables.

What should a residual plot look like?

• Random with no pattern.

• A clear upward trend.

• A clear downward trend.

• A parabolic shape.

What does a correlation coefficient of r = 1 indicate?

• A perfect positive linear relationship between two variables.

• No relationship between the two variables.

• A perfect negative linear relationship between two variables.

• A weak positive linear relationship between two variables.

Estimate the correlation coefficient for a strong negative association.

• r ≈ -0.2

• r ≈ -0.5

• r ≈ -0.8

• r ≈ -1.0

What is a residual in linear regression?

• The difference between the observed value and the predicted value from a regression model.

• The sum of all predicted values in a regression model.

• The average of the observed values in a regression model.

• The slope of the regression line.

What is the interpretation of the y-intercept in a linear regression equation?

• It represents the predicted value of the dependent variable when the independent variable is zero.

• It indicates the slope of the regression line.

• It shows the correlation between the independent and dependent variables.

• It represents the value of the independent variable when the dependent variable is zero.