Pearson Correlation Calculator
Calculate the Pearson correlation coefficient (r) and coefficient of determination (r2) for two data series. Enter values separated by commas — instant result with interpretation, no signup needed.
Current for 2026Methodology →
Linear Regression Calculator
This linear regression calculator determines the best-fit line y = ax + b through your data points. It computes the slope (a), intercept (b), coefficient of determination (R²), and a predicted Y value for any X you provide. Useful for statistics, data analysis, economics, and scientific research.
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How to Use the Linear Regression Calculator
Enter your X values separated by commas (e.g. 1,2,3,4,5) in the "X Series" field. Enter the corresponding Y values in the "Y Series" field. Enter the X value for which you want a prediction. Click "Calculate" to see the regression line equation and R².
Linear Regression Calculation Example
Given X = [1, 2, 3, 4, 5] and Y = [2.1, 3.9, 5.8, 7.2, 9.1], the calculator finds: a ≈ 1.75, b ≈ 0.38, R² ≈ 0.9993. The prediction for X = 6 is y ≈ 10.88. The near-perfect R² confirms a strong linear relationship.
Frequently Asked Questions
What is linear regression?
Linear regression is a statistical method that models the linear relationship between a dependent variable Y and an independent variable X using the equation y = ax + b.
What does the slope coefficient a represent?
The slope a indicates how much Y changes when X increases by one unit. A positive a means Y increases with X; a negative a means Y decreases.
What does the intercept b represent?
The intercept b is the value of Y when X equals zero. It indicates where the regression line crosses the Y-axis.
What is R² and how do I interpret it?
R² (coefficient of determination) measures how well the regression model fits the data. A value of 1.0 means a perfect fit; 0.0 means no linear relationship.
What is a good R² value?
It depends on the field. In natural sciences, R² > 0.95 is common. In social sciences, R² > 0.7 may be acceptable. Higher is generally better.
How many data points do I need?
At least 2 points are needed mathematically, but 5–10 or more are recommended for reliable results. More data improves model stability.
Can I separate values with semicolons or spaces?
Yes. The calculator accepts values separated by commas, semicolons, or spaces. Any consistent delimiter will work.
Is extrapolation reliable?
Extrapolating beyond the data range can be unreliable. The further from observed data, the greater the uncertainty. Use predictions with caution.
How does regression differ from correlation?
Correlation measures the strength of the linear relationship (r coefficient), while regression provides an equation for predicting Y from X. Both complement each other.
When should I not use linear regression?
Avoid linear regression when the relationship between X and Y is non-linear. A low R² or curved residual plot signals that a different model may be more appropriate.
Results are for informational purposes. Linear regression assumes a linear relationship between variables. For non-linear data or data with outliers, results may be less accurate.
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