Scatter Plot Calculator

Enter x,y data pairs to generate a scatter plot, compute correlation coefficient r, and find the least-squares regression line.

Enter Data Points

#XY

Scatter Plot & Results

Correlation Coefficient (r)
--
Number of Points--
Trend Line (y = mx + b)--
Slope (m)--
Y-Intercept (b)--
R-squared--
Mean X--
Mean Y--

Step-by-Step Calculation

Understanding Scatter Plots

A scatter plot (or scatter diagram) is a type of data visualization that uses Cartesian coordinates to display values for two variables. Each point represents one observation, with position determined by its x and y values. Scatter plots reveal relationships, patterns, and outliers in data.

Key Concepts

Correlation Coefficient (r)

Measures the strength and direction of the linear relationship between two variables. Range: -1 to +1.

r = sum((xi-x_mean)(yi-y_mean)) / sqrt(sum((xi-x_mean)^2)*sum((yi-y_mean)^2))

Least-Squares Regression

Finds the best-fit straight line through the data by minimizing the sum of squared residuals.

y = mx + b

R-Squared

The coefficient of determination. Represents the proportion of variance in y explained by x.

R^2 = r^2

Interpreting Correlation

  • r = 1: Perfect positive linear relationship.
  • r = -1: Perfect negative linear relationship.
  • r = 0: No linear relationship.
  • 0.7 to 1.0: Strong positive correlation.
  • -0.7 to -1.0: Strong negative correlation.