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

$\bar{x}$ 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.

Correlation indicates a relationship between variables, but does not prove that one variable causes the other. Other factors may be involved.

The correlation coefficient, r, is not resistant to outliers. A single outlier can drastically change the value of r.

r only measures linear relationships. A strong r doesn't mean there's no relationship, just no linear one.

Values of r closer to 1 or -1 indicate a stronger linear relationship, while values closer to 0 indicate a weaker linear relationship.

Enter x-values in L1 and y-values in L2. Go to STAT > CALC > LinReg(ax+b). Ensure 'DiagnosticOn' is enabled in the MODE menu to see the r value.

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.