Linear Regression Calculator (Simple & Multiple)

Linear regression predicts a continuous outcome (Y) from one predictor (simple regression) or several predictors (multiple regression), for example exam scores from study hours and sleep. Paste your data with Y in the first column and the calculator gives the same three tables as SPSS: Model Summary (R, R², adjusted R²), ANOVA, and Coefficients with B, standard errors, standardized β, t, p, 95% CIs and VIF, plus an APA 7 paragraph.

How to use this calculator

  1. Put the dependent variable (Y) in the first column and each predictor in the following columns.
  2. Include a header row with variable names for clearer output.
  3. Paste and click Calculate. Rows with missing values are excluded listwise.
  4. Check R², the ANOVA F test and each predictor’s p-value and VIF.

Formula

Y = b₀ + b₁X₁ + b₂X₂ + … + e
B = (XᵀX)⁻¹Xᵀy  (ordinary least squares)
R² = SS_regression / SS_total;  adjusted R² = 1 − (1 − R²)(n − 1)/(n − k − 1)
F = MS_regression / MS_residual;  t = B / SE(B);  β = B × SD(X) / SD(Y)
VIF = 1 / (1 − R²ⱼ)

Step-by-step example

  1. 12 students: exam score (Y), study hours (X₁) and hours of sleep (X₂).
  2. Exam = 42.11 + 4.11 × StudyHours + 0.59 × Sleep.
  3. R² = .986, adjusted R² = .983; F(2, 9) = 317.22, p < .001.
  4. Study hours: β = 0.95, p < .001; sleep: β = 0.06, p = .300 (not significant).

How to interpret the results

Start with the ANOVA table: a significant F means the model predicts Y better than the mean alone. R² is the proportion of variance in Y explained by the predictors; adjusted R² corrects for the number of predictors. Each B shows how much Y changes for a one-unit increase in that predictor, holding the others constant; β (standardized) lets you compare predictors measured on different scales. VIF values above 5–10 point to multicollinearity.

How to report it in APA 7 style

A multiple linear regression was conducted to predict exam scores from study hours and sleep. The model was statistically significant, F(2, 9) = 317.22, p < .001, and explained 98.6% of the variance (R² = .99, adjusted R² = .98). Study hours was a significant predictor (B = 4.11, β = 0.95, t = 17.13, p < .001), whereas sleep was not (B = 0.59, β = 0.06, t = 1.10, p = .300).

Statistical symbols (t, F, p, r, M, SD, N, d) should be italicised in your thesis.

Assumptions

  • Linear relationship between each predictor and Y.
  • Independent residuals (no autocorrelation).
  • Homoscedasticity: residuals have constant variance.
  • Residuals are approximately normally distributed.
  • No severe multicollinearity among predictors (check VIF).
  • No influential outliers.

How to do it in SPSS, R or Excel

SPSS: Analyze → Regression → Linear → Statistics → tick Confidence intervals and Collinearity diagnostics. R: summary(lm(y ~ x1 + x2)). Python: statsmodels.api.OLS, which ScholarCalc’s coefficients, p-values and VIF were validated against.

Roman Urdu mein khulasa

Regression batata hai ke predictors (X) dependent variable (Y) ko kitna predict karte hain. Excel mein pehla column Y aur baqi columns predictors rakhein. R² batata hai ke Y ki kitni variation predictors explain karte hain. Har predictor ka B batata hai ke X aik unit barhne par Y kitna badalta hai, aur β se predictors ki taqat compare ki jati hai. VIF 5 se zyada ho to predictors aapas mein bohat jure hue hain.

Frequently asked questions

What is the difference between simple and multiple regression?

Simple regression uses one predictor; multiple regression uses two or more predictors at the same time and shows each predictor’s unique contribution.

What is a good R² value?

It depends on the field. In social sciences, R² values of .10–.30 are common and can still be meaningful; in physical sciences much higher values are expected.

What is the difference between B and β?

B is the unstandardized coefficient in the original units of Y. β is standardized (in SD units), so you can compare the relative strength of predictors measured on different scales.

What does VIF tell me?

The variance inflation factor measures multicollinearity. Values above 5 (strict) or 10 (lenient) suggest that predictors overlap too much.

Can I use categorical predictors?

Yes, after coding them as dummy variables (0/1). For a variable with k categories, create k − 1 dummy columns.

How do I report a regression in APA?

Report the model F test, R² and adjusted R², then each predictor’s B, β, t and p, for example: F(2, 9) = 317.22, p < .001, R² = .99.

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Cite this calculator

If ScholarCalc helped your analysis, you can cite it in APA 7 format:

ScholarCalc. (2026). Linear Regression Calculator (Simple & Multiple) [Web application]. https://scholarcalc.com/linear-regression-calculator/

Written and maintained by the ScholarCalc team. Last reviewed: November 2026.

Accuracy: results are computed in your browser and were validated against Python scipy, statsmodels and pingouin on test datasets. See Methodology and accuracy.