Linear Regression Calculator - Free Statistical Analysis Tool
Linear Regression Calculator
Analyze the linear relationship between two variables. Find the best-fit line and make predictions.
Enter Your Data
Format: x, y (comma or space separated)
Regression Analysis Results
Regression Equation
R-Squared
Explained variance
Correlation (r)
Linear relationship
Std Error
Residual SE
Sample Size
Data points
Scatter Plot with Regression Line
Residual Plot
Check for patterns - residuals should be randomly scattered around zero
Coefficient Analysis
| Coefficient | Estimate | Std Error | t-value | p-value | 95% CI |
|---|
Make Predictions
Predicted Y value:
95% Prediction Interval:
95% Confidence Interval:
Data Summary
X Variable Statistics
Y Variable Statistics
How to use this calculator
📊 How to Use This Calculator
- Enter your data pairs (X and Y values)
- Name your variables for clearer results
- Click "Perform Regression Analysis"
- Review the regression equation and statistics
- Use the prediction tool to estimate new values
- Check residual plot for model assumptions
📐 Understanding Linear Regression
What is Linear Regression?
A statistical method to model the relationship between a dependent variable (Y) and independent variable (X) using a straight line.
The Regression Equation
Y = β₀ + β₁X + ε
- • β₀ = Y-intercept (value when X = 0)
- • β₁ = Slope (change in Y per unit change in X)
- • ε = Error term
Key Statistics
- • R²: Proportion of variance explained (0-1)
- • r: Correlation coefficient (-1 to +1)
- • Standard Error: Average prediction error
- • p-value: Test if slope is significantly different from 0
🌟 Real-World Examples
Example 1: Sales vs Advertising
X = Advertising spend ($1000s), Y = Sales ($1000s)
Equation: Sales = 50 + 2.5 × Advertising
Interpretation: Each $1000 in advertising increases sales by $2500
Example 2: Height vs Weight
X = Height (inches), Y = Weight (pounds)
Equation: Weight = -200 + 5 × Height
R² = 0.65 means height explains 65% of weight variation
Example 3: Study Time vs Exam Score
X = Study hours, Y = Exam score (%)
Equation: Score = 60 + 3 × Hours
Each hour of study increases score by 3 points
💡 Pro Tips
- • Check residual plot for patterns - should be random
- • R² close to 1 indicates strong linear relationship
- • Watch for outliers - they can heavily influence results
- • Prediction intervals are wider than confidence intervals
- • Don't extrapolate beyond your data range
- • Consider transformations if relationship is non-linear
⚠️ Common Mistakes to Avoid
- • Correlation does not imply causation
- • Don't ignore assumptions (linearity, normality, etc.)
- • Avoid overfitting with too few data points
- • Check for influential points and outliers
- • Don't use regression for non-linear relationships
- • Be cautious with extrapolation outside data range
About this calculator
Perform linear regression analysis. Calculate slope, intercept, R-squared, predictions, and residuals with scatter plot visualization.
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