AP Stats 3.1-3.2 Regression & Correlation

Front

What is correlation?

Back

Correlation is a statistical measure that describes the extent to which two variables change together. A positive correlation means that as one variable increases, the other also increases, while a negative correlation means that as one variable increases, the other decreases.

Front

What does a correlation coefficient (r) of 0 indicate?

Back

A correlation coefficient (r) of 0 indicates no correlation between the two variables.

Front

What does the coefficient of determination (r²) represent?

Back

The coefficient of determination (r²) represents the proportion of the variance in the dependent variable that is predictable from the independent variable.

Front

How do you interpret an r² value of 0.85?

Back

An r² value of 0.85 means that 85% of the variability in the dependent variable can be explained by the independent variable.

Front

What is a residual in regression analysis?

Back

A residual is the difference between the observed value and the predicted value of the dependent variable.

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How do you calculate a residual?

Back

Residual = Observed value - Predicted value.

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What does a residual plot show?

Back

A residual plot shows the residuals on the vertical axis and the independent variable on the horizontal axis, helping to assess the fit of a regression model.

Front

What indicates a strong positive correlation in a scatter plot?

Back

A strong positive correlation in a scatter plot is indicated by points that closely follow a straight line with a positive slope.

Front

What indicates a strong negative correlation in a scatter plot?

Back

A strong negative correlation in a scatter plot is indicated by points that closely follow a straight line with a negative slope.

Front

What is the purpose of a least squares regression line?

Back

The least squares regression line minimizes the sum of the squares of the residuals, providing the best fit for the data.