Format: each line is "x, y" or "x y". At least 2 points required.
Linear regression is one of the most fundamental and widely used statistical techniques in data science, machine learning, economics, and scientific research. It models the relationship between a dependent variable (often called the response or target variable) and one or more independent variables (predictors or features) by fitting a linear equation to observed data. Simple linear regression involves a single independent variable, producing a straight line described by the equation y = mx + b, where m is the slope and b is the y-intercept. Multiple linear regression extends this concept to multiple predictors. Linear regression is used for trend analysis, forecasting, risk assessment, and understanding relationships between variables in fields ranging from finance and marketing to biology and engineering. The quality of a linear regression model is assessed using metrics like R-squared (coefficient of determination), which indicates how much of the variance in the dependent variable is explained by the model. Our Linear Regression Calculator allows you to input data points, instantly computes the regression line, and visualizes the results with an interactive chart.
Enter your data as pairs of x and y values. You can input data in several formats: comma-separated pairs (e.g., '1,2 3,5 5,8'), one pair per line, or paste a table from a spreadsheet. The tool automatically parses your input and validates the data. Each x-y pair represents one observation or measurement. There is no minimum number of data points required, though at least two points are needed to calculate a regression line, and more points produce more reliable results. You can also load sample datasets to explore how the tool works before entering your own data.
Click the 'Calculate' button to perform the linear regression analysis. The tool uses the ordinary least squares (OLS) method, which minimizes the sum of squared differences between observed and predicted values. The calculation produces the slope (m), y-intercept (b), the regression equation (y = mx + b), the R-squared value, and the correlation coefficient (r). The slope tells you how much y changes for each unit increase in x, the intercept tells you the predicted y value when x is zero, and R-squared tells you how well the line fits your data — values closer to 1 indicate a better fit.
The results are presented both numerically and visually. A scatter plot shows your data points with the regression line overlaid, making it easy to see how well the line fits the data and identify any outliers. The equation and key statistics are displayed alongside the chart. If your R-squared is above 0.7, the linear model explains most of the variance and is likely a good fit. Lower values suggest the relationship may be non-linear or that other factors are influencing the dependent variable. You can hover over data points on the chart to see their exact values, and the visualization updates dynamically if you modify your data.
R-squared (also called the coefficient of determination) measures the proportion of variance in the dependent variable that is explained by the independent variable in your regression model. It ranges from 0 to 1 (or 0% to 100%). An R-squared of 0 means the model explains none of the variance, while 1 means it explains all of it. In practice, what constitutes a 'good' R-squared depends heavily on the field. In physics and engineering, R-squared above 0.9 is often expected. In social sciences and marketing, 0.3 to 0.5 may be considered meaningful. A high R-squared does not necessarily mean the model is correct — it could be overfitting or the relationship might be non-linear with a coincidentally high linear correlation.
Correlation measures the strength and direction of a linear relationship between two variables, producing a value between -1 and 1. It does not imply causation or predict values. Linear regression goes further by modeling the relationship with an equation (y = mx + b) that can predict y values for given x values. Correlation tells you whether variables are related; regression tells you how they are related and by how much. Another key difference: correlation is symmetric (the correlation between x and y equals the correlation between y and x), but regression is not — regressing y on x produces a different line than regressing x on y.
Linear regression assumes a linear relationship between variables, so it performs poorly when the true relationship is curved or non-linear (e.g., exponential growth, logarithmic decay, periodic patterns). It is also sensitive to outliers — a single extreme data point can significantly skew the regression line. Linear regression assumes that residuals (differences between predicted and actual values) are normally distributed and have constant variance (homoscedasticity). If these assumptions are violated, the results may be unreliable. For non-linear relationships, consider polynomial regression, logistic regression (for binary outcomes), or other specialized techniques.