Linear Regression Calculator

• •Use the Linear Regression Calculator to check your hand calculations on homework or exam problems — comparing its result with your own working helps identify arithmetic errors before they propagate.
• •Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
• •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
• •Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
• •Use it in the field when a quick estimate is needed and a full engineering software package is not available.

The Linear Regression Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. Simple linear regression with slope, intercept, R², adjusted R², residuals, predictions, and scatter/residual plots All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Follow the units printed beside each field. Where a unit selector is provided, the selected unit is converted internally. Results are computed in your browser without sending data to a server, which keeps your inputs private. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.

Simple linear regression fits a straight line y = β₀ + β₁·x + ε to data, minimizing the sum of squared residuals (method of least squares). The slope β₁ = Σ((x − x̄)(y − ȳ)) / Σ(x − x̄)² and the intercept β₀ = ȳ − β₁·x̄. The coefficient of determination R² = 1 − SS_residual/SS_total measures the proportion of variance in y explained by x, ranging from 0 (no fit) to 1 (perfect fit). The adjusted R² accounts for the number of predictors: R²_adj = 1 − (1 − R²)·(n−1)/(n−p−1), where p is the number of predictors. For simple linear regression, p = 1. Standard errors of the coefficients quantify uncertainty: SE(β₁) = √(MSE/Σ(x − x̄)²) and SE(β₀) similarly. Hypothesis tests on β₁ use t = β₁/SE(β₁), which follows a t-distribution with n−2 degrees of freedom. Confidence intervals on β₁ are β₁ ± t_(α/2, n−2)·SE(β₁). The regression assumes: (1) linearity — y is a linear function of x; (2) independence — observations are independent; (3) homoscedasticity — residuals have constant variance; (4) normality — residuals are normally distributed. Violations require transformations, weighted regression, or non-parametric methods. For multiple predictors, use multiple linear regression with matrix computations. The calculator handles simple linear regression with slope, intercept, R², SE, and prediction intervals.

• •Calibration curves: relate instrument readings (x) to actual values (y) from calibration standards, then use the regression to convert new readings to values.
• •Trend analysis: fit linear trend to time-series data (revenue, temperature, performance metrics) to quantify direction and rate of change.
• •Predictive modeling: predict one variable from another using the fitted regression, with prediction intervals quantifying uncertainty.
• •Quality control: relate process variables to output variables and identify which process factors control product quality.
• •Scientific data analysis: fit experimental data to a theoretical linear relationship to estimate the slope (often a physical constant) and test agreement.