Correlation - AP Statistics

Weak positive correlation. Close to zero indicates weak linear association.

Strong negative correlation. Close to -1 indicates strong negative linear relationship.

$r = \frac{\sum((x_i - \bar{x})(y_i - \bar{y}))}{\sqrt{\sum(x_i - \bar{x})^2 \cdot \sum(y_i - \bar{y})^2}}$. Standardized covariance using sample standard deviations.

As one variable increases, the other tends to increase. Strong positive correlation shows variables move together.

As one variable increases, the other tends to decrease. Strong negative correlation shows variables move opposite.

Variables should have a linear relationship. Pearson's $r$ requires approximately linear relationships.

It can significantly distort the correlation coefficient. Outliers can inflate or deflate correlation strength.

No, correlation does not imply causation. Association does not establish cause-and-effect relationship.

Very strong positive correlation. Extremely close to 1 indicates nearly perfect positive relationship.

Weak negative correlation. Very close to zero indicates minimal linear relationship.

Correlation measures the strength and direction of a linear relationship between two variables. Quantifies linear association between two quantitative variables.

No linear relationship between variables. Zero correlation means no linear pattern exists.

Perfect positive linear correlation. All points lie exactly on a positive-sloped line.

Perfect negative linear correlation. All points lie exactly on a negative-sloped line.

A correlation that appears real but is caused by a third variable. Confounding variables create misleading correlations.

To visually assess the relationship between two variables. Graphically displays correlation patterns and outliers.

It can lead to underestimating the true correlation. Limited data range reduces correlation variability.

$\rho$ (rho). Greek letter rho represents population parameter.

Correlation may underestimate the relationship. Non-linear patterns reduce apparent correlation strength.

No linear correlation. Exactly zero means no linear relationship exists.

Moderate to strong negative correlation. Between moderate and strong negative correlation range.

Moderate positive correlation. Halfway between zero and one indicates moderate strength.

It is unitless and unaffected by unit changes. Standardized measure independent of measurement units.

Stronger correlation improves prediction accuracy. Higher correlation improves predictive model accuracy.

The Pearson correlation significance test. Tests if population correlation differs from zero.

Proportion of variance explained by the relationship. Squared correlation shows shared variance between variables.

Moderate positive correlation. Close to 0.5 indicates moderate positive linear relationship.

It does not account for causality. Cannot determine which variable influences the other.

Weak positive correlation. Weak but positive linear association between variables.