AP Stats Chapter 3 Multiple Choice Review

Front

What does a correlation coefficient (r) of 0.51 indicate about the relationship between two variables?

Back

A correlation coefficient (r) of 0.51 indicates a moderate positive linear relationship between the two variables.

Front

How is the percentage of variation explained by the least squares regression line calculated from the correlation coefficient?

Back

The percentage of variation explained is calculated as r² (the square of the correlation coefficient). For r = 0.51, r² = 0.2601, or approximately 26%.

Front

What effect do outliers have on the correlation coefficient?

Back

Outliers can significantly affect the correlation coefficient, potentially skewing the value and misrepresenting the strength of the relationship.

Front

What is the relationship between correlation coefficients r1, r2, and r3 if r2 < r1 < r3?

Back

This indicates that the strength of the correlation increases from r2 to r1 to r3, meaning r3 represents the strongest correlation among the three.

Front

What can be concluded about the correlation when points on a scatterplot form an ellipse?

Back

When points form an ellipse, the correlation is not strong; as the ellipse becomes thinner, the correlation may increase, but no definitive conclusion can be drawn without further analysis.

Front

What is the range of possible values for a correlation coefficient?

Back

The range of possible values for a correlation coefficient is from -1 to 1.

Front

What does a correlation coefficient of 1 indicate?

Back

A correlation coefficient of 1 indicates a perfect positive linear relationship between two variables.

Front

What does a correlation coefficient of -1 indicate?

Back

A correlation coefficient of -1 indicates a perfect negative linear relationship between two variables.

Front

What is the purpose of a least squares regression line?

Back

The least squares regression line is used to predict the value of a dependent variable based on the value of an independent variable by minimizing the sum of the squares of the residuals.

Front

What is the difference between correlation and causation?

Back

Correlation indicates a relationship between two variables, while causation implies that one variable directly affects the other.