Linear Regression Calculator
What is Linear Regression?
Linear regression is a statistical method used to model the relationship between a dependent variable (Y) and an independent variable (X) by fitting a linear equation to observed data. The relationship is expressed as Y = mX + b, where m is the slope and b is the y-intercept.
This calculator performs linear regression analysis to find the best-fit line through your data points, calculates correlation coefficients, and allows you to make predictions based on the regression equation.
Key Components:
- Slope (m): Rate of change in Y for each unit change in X
- Y-intercept (b): Value of Y when X equals zero
- Correlation (r): Strength and direction of linear relationship (-1 to 1)
- R-squared (r²): Proportion of variance explained by the model (0 to 1)
How It Works
Enter Data
Input X and Y values
Calculate
Get regression line
Analyze
View correlation
Common Examples
Sales vs Advertising
Analyze relationship between advertising spend and sales revenue.
Temperature vs Ice Cream Sales
Predict ice cream sales based on temperature.
Calculation Table
| Formula | Description |
|---|---|
| m = (n∑xy - ∑x∑y) / (n∑x² - (∑x)²) | Slope calculation |
| b = (∑y - m∑x) / n | Y-intercept calculation |
| r = (n∑xy - ∑x∑y) / √[(n∑x² - (∑x)²)(n∑y² - (∑y)²)] | Correlation coefficient |
| r² = r × r | Coefficient of determination |
| y = mx + b | Linear regression equation |
Frequently Asked Questions
What is linear regression used for?
Linear regression is used to model relationships between variables, make predictions, analyze trends, and understand how one variable affects another. Common applications include sales forecasting, risk analysis, and scientific research.
How do I interpret the correlation coefficient?
The correlation coefficient (r) ranges from -1 to 1. Values close to 1 indicate strong positive correlation, values close to -1 indicate strong negative correlation, and values near 0 indicate weak or no linear relationship.
What does R-squared tell me?
R-squared (r²) represents the proportion of variance in the dependent variable explained by the independent variable. For example, r² = 0.8 means 80% of the variation in Y is explained by X.
How many data points do I need?
You need at least 2 data points for linear regression, but more points (typically 10+ for reliable results) provide better accuracy and more meaningful statistical measures.
Can I use this for non-linear relationships?
This calculator performs linear regression only. For non-linear relationships, you would need polynomial regression, exponential regression, or other advanced statistical methods.