Scatter Plot and Correlation Explorer

Enter x, y data pairs to visualize bivariate data, compute Pearson correlation coefficient (r and r²), and fit a linear regression line. Choose from presets or enter your own data.

Scatter Plot

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Data Input

Format: x, y per line. Example: 3.5, 72.1

13 points loaded

Results

Pearson r

0.9925

r²

0.9850

Slope

8.1538

Intercept

40.8462

Regression Line

y = 8.1538x +40.8462

Interpretation

Very strong positive correlation (n = 13)

r² = 98.5% of the variance in y is explained by x.

Correlation Strength

-10+1

Reference Guide

Pearson Correlation Coefficient

The Pearson r measures the linear relationship between two variables. It ranges from -1 (perfect negative) to +1 (perfect positive), with 0 meaning no linear relationship.

r=∑(xi−xˉ)(yi−yˉ)∑(xi−xˉ)2∑(yi−yˉ)2r = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum(x_i-\bar{x})^2 \sum(y_i-\bar{y})^2}}
  • |r| >= 0.9: Very strong
  • |r| >= 0.7: Strong
  • |r| >= 0.5: Moderate
  • |r| >= 0.3: Weak
  • |r| below 0.3: Very weak

Linear Regression

The regression line minimizes the sum of squared residuals (ordinary least squares). It gives the best linear predictor of y given x.

y^=mx+b\hat{y} = m x + b
m=∑(xi−xˉ)(yi−yˉ)∑(xi−xˉ)2,b=yˉ−mxˉm = \frac{\sum(x_i-\bar{x})(y_i-\bar{y})}{\sum(x_i-\bar{x})^2}, \quad b = \bar{y} - m\bar{x}

Interpreting r²

The coefficient of determination r² tells you the proportion of variance in y that is explained by x. For example, r² = 0.81 means 81% of the variation in y is accounted for by the linear relationship with x.

r2=1−SSresSStotr^2 = 1 - \frac{SS_{\text{res}}}{SS_{\text{tot}}}

r² ranges from 0 (no explanatory power) to 1 (perfect fit). Correlation does not imply causation.