A value, r, that measures the strength and direction of a linear relationship between two variables. Ranges from -1 to 1.

A relationship where as one variable increases, the other tends to increase.

A relationship where as one variable increases, the other tends to decrease.

No linear correlation between the two variables.

A graphical representation of the relationship between two variables.

$r = \frac{1}{n-1} \sum_{i=1}^{n} (\frac{x_i - \bar{x}}{s_x}) (\frac{y_i - \bar{y}}{s_y})$

$\bar{x}$ and $\bar{y}$ are the means of the x and y variables, respectively.

$s_x$ and $s_y$ are the standard deviations of the x and y variables, respectively.

n is the number of data points.

$\sum$ represents the summation of the expression that follows.

r = 1: Perfect positive correlation (points form an exact increasing line). | r = -1: Perfect negative correlation (points form an exact decreasing line).

Positive Correlation: As one variable increases, the other tends to increase. | Negative Correlation: As one variable increases, the other tends to decrease.

Correlation: Measures the strength and direction of a relationship between two variables. | Causation: Indicates that one variable directly causes a change in another variable.

Linear Relationships: Can be accurately described by a straight line; correlation coefficient r is applicable. | Non-Linear Relationships: Cannot be accurately described by a straight line; correlation coefficient r may be misleading.

Strong Correlation: Points on a scatterplot cluster closely around a line; r is close to 1 or -1. | Weak Correlation: Points on a scatterplot are more scattered; r is closer to 0.