# Linear Regression Calculator Fit a simple least-squares linear regression model and calculate slope, intercept, R squared, and predictions > Canonical page: https://elysiatools.com/en/tools/linear-regression-calculator - **Category:** Math & Numbers - **Keywords:** linear regression, least squares, slope, intercept, r squared, calculator ## Overview The Linear Regression Calculator is a specialized tool designed to fit a simple least-squares regression model to your data. It provides essential statistical metrics, including the slope, y-intercept, and R-squared value, while allowing you to generate precise predictions for specific X values based on the calculated trend line. ## Inputs - **Data Pairs** (textarea): One pair per line, e.g. 1, 2 2, 4 3, 5 - **X Values (Optional)** (text): Alternative input: 1, 2, 3, 4 - **Y Values (Optional)** (text): Alternative input: 2, 3, 5, 7 - **Prediction X (Optional)** (text): e.g. 6 - **Decimal Places** (number) ## When to use - When you need to determine the mathematical relationship between two continuous variables. - When evaluating the strength of a linear correlation using the R-squared coefficient. - When predicting future outcomes or missing values based on historical data trends. ## How it works - Input your data as coordinate pairs (X, Y) or as separate lists of X and Y values. - Specify an optional X value if you wish to calculate a specific Y prediction based on the fitted model. - Set the desired number of decimal places for the output results to ensure numerical precision. - The tool applies the least-squares method to minimize the sum of squared residuals and returns the model parameters in JSON format. ## Use cases - Analyzing the correlation between advertising spend and monthly sales revenue. - Estimating crop yields based on varying levels of rainfall or fertilizer application. - Predicting student test scores based on the number of hours spent studying. ## Frequently asked questions ### What is the R-squared value? It is the coefficient of determination that measures how well the linear regression model fits the data, with 1.0 representing a perfect fit. ### Can I input data in different formats? Yes, you can provide data as line-separated pairs or as two distinct lists of X and Y values. ### What does the slope represent? The slope indicates the average change in the Y variable for every one-unit increase in the X variable. ### Is there a limit to the number of data points? The tool handles standard datasets efficiently; you must provide at least two pairs to calculate a valid regression line. ### What is the intercept? The intercept is the predicted value of Y when the X value is zero, representing where the line crosses the Y-axis. ## Related tools - [Bayes Theorem Calculator](https://elysiatools.com/en/tools/bayes-theorem-calculator): Calculate posterior probability P(A given B) using prior, likelihood, and false-positive rate - [Bearing Capacity Calculator (Terzaghi)](https://elysiatools.com/en/tools/bearing-capacity-calculator): Calculate the Terzaghi ultimate bearing capacity of a shallow foundation: q_ult = c·Nc·sc + q·Nq·sq + 0.5·γ·B·Nγ·sγ. Computes Nc/Nq/Nγ and shape factors automatically; supports strip, square, and circular footings. Result in kPa. - [Belt Pulley Speed Ratio Calculator](https://elysiatools.com/en/tools/belt-pulley-speed-ratio): Calculate the ratio, driven speed and belt linear speed of a belt drive. i = d₂/d₁ = n₁/n₂, belt speed v = π·d·n/60. 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