Least Squares Regression Calculator
Find the line of best fit using least squares method with correlation analysis
Enter Data Points
Valid data points: 2 / 2
Least Squares Method
Calculate distances
Find vertical distances from points to line
Square the distances
Square each distance to eliminate negatives
Minimize sum
Find line that minimizes sum of squared errors
Key Formulas
Tips
R² close to 1 indicates strong linear relationship
Watch out for outliers that can skew results
More data points generally improve accuracy
Consider non-linear models for curved relationships
Understanding Least Squares Regression
What is Least Squares Regression?
Least squares regression is a statistical method used to find the line of best fit through a set of data points. It minimizes the sum of squared vertical distances between the observed data points and the fitted line.
Why Use This Method?
- •Provides the best linear unbiased estimate
- •Widely accepted and mathematically robust
- •Easy to interpret and implement
- •Foundation for more complex statistical models
Applications
Economics & Finance
Predicting stock prices, analyzing market trends
Science & Engineering
Calibrating instruments, modeling physical phenomena
Machine Learning
Linear regression models, feature selection
Quality Control
Process optimization, trend analysis
Understanding the Results
Correlation Coefficient (r)
- r = 1: Perfect positive correlation
- r = 0: No linear correlation
- r = -1: Perfect negative correlation
- |r| > 0.8: Strong correlation
- |r| < 0.3: Weak correlation
R-Squared (R²)
- R² = 1: Perfect fit (100% variance explained)
- R² = 0: No explanatory power
- R² > 0.7: Good fit
- R² < 0.3: Poor fit
- Represents proportion of variance explained