Linear Regression Calculator

Calculate linear regression equation, correlation coefficient, and R-squared value for your data

Linear Regression Analysis

Data Points (x, y)

1.
2.
3.

Example Calculation

Sample Data

Data points: (1, 3), (2, 6), (3, 6)

Goal: Find the linear regression equation

Results

Regression equation: y = 1.5x + 2

R-squared: 0.75

Correlation: 0.866

Interpretation: 75% of variance in Y is explained by X

Key Concepts

Slope (a)

Change in Y per unit change in X

Intercept (b)

Y value when X = 0

R-squared (R²)

Proportion of variance explained (0 to 1)

Correlation (r)

Strength of linear relationship (-1 to 1)

R² Interpretation

R² > 0.7: Strong relationship
0.3 < R² < 0.7: Moderate
R² < 0.3: Weak relationship

Formulas

Slope:

a = Σ(xy) - nxy̅ / Σ(x²) - nx̅²

Intercept:

b = y̅ - ax̅

Correlation:

r = a × (sx / sy)

Understanding Linear Regression

What is Linear Regression?

Linear regression is a statistical method that models the relationship between two variables by fitting a linear equation to observed data. It finds the line that best predicts the dependent variable (Y) based on the independent variable (X).

Key Applications

  • Predicting sales based on advertising spend
  • Analyzing the relationship between height and weight
  • Forecasting stock prices or economic trends
  • Medical research and dose-response studies

Interpreting Results

Slope Interpretation

The slope tells you how much Y changes when X increases by 1 unit. Positive slopes indicate Y increases as X increases.

R-squared Interpretation

R² ranges from 0 to 1. Higher values indicate the model explains more of the variance in your data. R² = 0.8 means 80% of the variance is explained.

Correlation Coefficient

Values closer to +1 or -1 indicate stronger linear relationships. Values near 0 suggest weak linear relationships.

Important Notes

  • • Linear regression assumes a linear relationship between variables
  • • Check residual plots to validate model assumptions
  • • Correlation does not imply causation
  • • Outliers can significantly affect the regression line