APEX AP Stats 3.3.1 Pearson Correlation Coefficient Study Guide

What does Pearson's Correlation Coefficient (r) measure?

The direction and strength of the linear relationship between two variables and ranges from -1 to +1

Correlation

measures the amount of linear association between x and y values

What does a Pearson's r value close to -1 or +1 indicate?

A strong linear relationship between the two variables.

What does a Pearson's r value near 0 indicate?

A weak linear relationship between the variables.

What is a strong negative correlation?

As x increases, y decreases.

What is a strong positive correlation?

As x increases, y increases.

What characterizes no correlation?

The linear regression isn't meaningful and there isn't a linear relationship between the variables.

How are correlation coefficients categorized based on their values?

Strong: -0.7 to -1 and +0.7 to +1 Moderate: -0.3 to -0.7 and +0.3 to +0.7 Weak: -0.3 to 0 and +0.3 to 0.

What does the sign of Pearson's r represent?

The direction of the slope of the regression line.

What does it mean if the data points fall on a vertical or horizontal line?

It may indicate that something absurd is going on and the plot is useless.

What happens to Pearson's r if you switch the explanatory and response variables?

Pearson's r remains the same.

What is the formula for Pearson's r?

The product of (xi-x-bar/sx)(y-y-bar/sy) multiplied by 1/n-1. xi - x-bar = the standardized value of xi yi - y-bar = the standardized value of yi

What does r^2 represent?

The coefficient of determination, showing the percentage of variation in y explained by the variation in x.

What does a high correlation coefficient r suggest about cause and effect?

It suggests a potential cause-and-effect relationship, but does not prove it.

What is the significance of the point (x-bar, y-bar) in regression analysis?

It always lies on the least squares regression line.

What is the relationship between the slope (b1) and the correlation coefficient (r)?

b1 = r(sy/sx). b1=slope of line/regression coefficient r=correlation coefficient sy=standard deviation of y sx= standard deviation of x

What is the correction factor used when calculating r from sample data?

1/n-1.

What should you do to calculate r from sample data?

Create a scatterplot and linear regression line, then determine the correlation coefficient.

What does a perfect correlation (r = +1 or -1) indicate?

All data points fall on a straight line; aka perfect positive/negative correlation

What is the implication of correlation not equating to causation?

High correlation does not imply that one variable causes changes in another.