Multiple linear regression calculator
Paste rows of numbers and fit an ordinary least-squares regression: the fitted equation, a coefficient table with standard errors, t-stats, p-values and confidence intervals, plus R², adjusted R² and the overall F-test. Runs entirely in your browser, nothing is uploaded.
About this tool
This multiple linear regression calculator fits an ordinary least-squares (OLS) model
y = b₀ + b₁·x₁ + … + bₖ·xₖ to a data matrix you paste in — one observation per line, columns
separated by commas, tabs, semicolons or spaces. By default the last column is the response
(dependent variable) y and every other column is a predictor; point response at first or a
1-based column number to pick a different Y. Give the columns real names with labels so the
coefficient table and equation read in your terms (sqft, rooms, price) instead of v1, v2, v3.
For each coefficient — including the intercept — you get the estimate, its standard error, the t-statistic, the two-tailed p-value (H₀: the coefficient is zero) and a confidence interval at your chosen level. At the model level it reports R² and adjusted R² (which penalises extra predictors), the residual standard error with its degrees of freedom, and the overall F-test with its p-value — the joint test that at least one predictor matters. Switch the output to JSON to additionally get the per-observation fitted values and residuals for diagnostics. Everything runs in your browser; your data never leaves the page.
Worked example
Input (data, with labels = sqft,rooms,price, so price is the response):
1,1,6
2,1,8
3,2,11
4,2,14
5,3,18
6,3,20
Output:
price = 2 + 2.333333·sqft + 1.333333·rooms
Coefficients:
term estimate std error t p 95% CI
(Intercept) 2 0.559384 3.575424 0.037461 [0.219859, 3.780141]
sqft 2.333333 0.3849 6.062178 0.009007 [1.108218, 3.558449]
rooms 1.333333 0.930949 1.432222 0.247544 [-1.62904, 4.295707]
(exact numbers are shown in full on the page) — with R² = 0.995638, adjusted R² = 0.99273
and an F-statistic of 342.375 on 2 and 3 DF (p = 0.000288), both predictors are strongly
significant and the model explains almost all of the variation in price.
Controls
- Response column —
last(default, rightmost),first, or a 1-based column index; every other column becomes a predictor. - Column names — optional comma-separated labels in data order; default
v1, v2, …. - Fit an intercept — on by default. Uncheck to force a zero Y-intercept (regression through the origin); this also switches R² to the uncentered definition, as statistical software does.
- Confidence level — for the coefficient intervals (default
0.95); the two-tailed significance level is α = 1 − level. - Output — a formatted summary, or JSON that adds the fitted values and residuals.
Limits and edge cases
- You need more observations than parameters (rows > predictors + intercept), otherwise the residual degrees of freedom would be zero or negative and the fit is rejected.
- Predictors must not be perfectly collinear (one an exact linear combination of others) — the normal-equations matrix is then singular and the model is not identifiable, so the tool errors instead of returning unstable numbers.
- Every value must be a finite number and every row must have the same number of columns; blank lines are ignored.
- All predictors are treated as numeric — encode categorical variables as dummy (0/1) columns and apply any log/sqrt transforms yourself before pasting.
- p-values and confidence intervals assume the usual OLS conditions (independent, homoscedastic, roughly normal residuals); check the residuals (JSON output) before trusting them.
FAQ
How do I choose which column is the dependent variable (Y)?
By default the last (rightmost) column is the response and everything to its left is a
predictor — the convention most calculators use. Set the response field to first for the first
column, or to a 1-based column number (2 = the second column) to use any other. Whichever
column you pick becomes y; all remaining columns are entered as predictors together.
What is the difference between R² and adjusted R²?
R² is the share of the variance in y explained by the model, from 0 to 1. It can only go up when you add predictors, even useless ones, so it rewards a bigger model unfairly. Adjusted R² corrects for that by penalising each extra predictor relative to the sample size, so it can fall when a predictor adds nothing. Use adjusted R² when comparing models with different numbers of predictors.
What does the p-value on each coefficient mean?
It is the two-tailed probability, under the null hypothesis that the true coefficient is zero, of seeing a t-statistic at least as extreme as the one observed. A small p-value (say below your α = 1 − confidence level) is evidence the predictor has a non-zero effect holding the other predictors fixed. The overall F-test is the joint version: it asks whether the predictors together explain more than chance would.
Why does forcing a zero intercept change my R²?
With an intercept, R² is computed against the mean of y (centered total sum of squares). When you force the line through the origin there is no intercept to absorb the mean, so software — this tool included — switches to the uncentered total sum of squares. The two R² values are not comparable, and a no-intercept R² is often much higher for reasons that have nothing to do with fit quality, so interpret it with care.
Why did I get a "perfectly collinear" or "not enough observations" error?
OLS needs the predictor matrix to be full rank. Perfect collinearity — one predictor being an exact linear combination of the others (e.g. a column that is another times a constant, or dummy columns that sum to 1) — makes the system unsolvable, so the tool stops instead of printing meaningless coefficients. You also need more rows than parameters; with as many parameters as observations the model would fit perfectly with zero residual degrees of freedom and no way to estimate uncertainty. Add rows or drop a redundant predictor.
Developer & Automation Access
Run it from the terminal
Same engine as this page, headless — via the gizza CLI:
gizza tool multiple-regression "1,6
2,8
3,11
4,14
5,18
6,20"New to the CLI? Get gizza →
Open it by URL
Pre-fill and auto-run this tool with query parameters — the names match the API/CLI:
https://gizza.ai/tools/multiple-regression/?data=1%2C6%0A2%2C8%0A3%2C11%0A4%2C14%0A5%2C18%0A6%2C20&response=last&labels=sqft%2Crooms%2Cprice&intercept=true&conf_level=0.95&format=textMachine-readable descriptor: tool.json — title + parameters JSON Schema for agents.