Simple Linear Regression Calculator
Predict an outcome from one predictor with ordinary least squares. You get the regression equation, R², significance tests and a residual plot.
Updated · By Bibin XavierData 90 × 12
| IDtext · 90 levels | Grouptext · 3 levels | Gendertext · 2 levels | Agenumeric | Hours_Studynumeric | Anxietynumeric | Motivationnumeric | Pre_Scorenumeric | Post_Scorenumeric | Exam_Scorenumeric | Passednumeric · coded | Satisfactionnumeric · coded |
|---|---|---|---|---|---|---|---|---|---|---|---|
| S001 | Control | Male | 23 | 11.2 | 29 | 4.6 | 60 | 62 | 67 | 1 | 2 |
| S002 | Workshop | Female | 23 | 3.9 | 28 | 3.5 | 54 | 70 | 54 | 0 | 2 |
| S003 | Online | Female | 18 | 10.1 | 32 | 4 | 55 | 57 | 66 | 0 | 3 |
| S004 | Control | Male | 26 | 13.6 | 41 | 3.5 | 52 | 55 | 59 | 0 | 3 |
| S005 | Workshop | Female | 22 | 9.7 | 27 | 3.6 | 56 | 63 | 65 | 0 | 4 |
| S006 | Online | Female | 20 | 7.9 | 32 | 3.8 | 65 | 82 | 65 | 0 | 2 |
| S007 | Control | Female | 20 | 6.3 | 28 | 3 | 72 | 83 | 61 | 0 | 3 |
| S008 | Workshop | Male | 22 | 8 | 29 | 3.1 | 64 | 72 | 62 | 1 | 3 |
Variables and options
Results
90 rows · example dataCoefficients
| B | SE | β | t | p | 95% CI | |
|---|---|---|---|---|---|---|
| (Intercept) | 49.459 | 3.638 | 13.60 | < .001 | [42.230, 56.688] | |
| Hours_Study | 1.258 | 0.345 | .362 | 3.64 | < .001 | [0.572, 1.944] |
ANOVA
| Source | SS | df | MS | F | p |
|---|---|---|---|---|---|
| Regression | 1013.58 | 1 | 1013.58 | 13.27 | < .001 |
| Residual | 6722.48 | 88 | 76.39 | ||
| Total | 7736.06 | 89 |
Note. Durbin-Watson = 1.98.
Scatter plot with regression line
Residuals against fitted values
Interpretation
Each one-unit increase in Hours_Study is associated with a 1.26-point increase in Exam_Score. Hours_Study explains 13.1% of the variance in Exam_Score, and the model is statistically significant. Residuals scattered evenly around zero support the linearity and equal-variance assumptions.
How to cite this tool
Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.
APA 7
Xavier, B. (2026). Simple Linear Regression Calculator [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/linear-regression-calculator/
BibTeX
@software{xavier_simplelinearregression_2026,
author = {Xavier, Bibin},
title = {Simple Linear Regression Calculator},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/linear-regression-calculator/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free Simple Linear Regression Calculator tool on FreeStatisticalTools.com (Xavier, 2026).”
What is simple linear regression?
Simple linear regression fits the straight line that best predicts an outcome Y from a predictor X by least squares. You get the equation, the significance of the slope, R² and diagnostic plots.
When to use simple linear regression
Use it to describe or predict a continuous outcome from one continuous predictor.
Assumptions
- A linear relationship.
- Independent residuals (Durbin-Watson near 2).
- Constant residual variance and approximately normal residuals.
How to use this tool
- Enter your data. Paste columns from Excel, Google Sheets or SPSS with variable names in the first row, or upload a CSV or Excel file. The example data shows the expected layout.
- Choose the variables. Select the predictor (x) and outcome (y).
- Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.
How to report simple linear regression in APA style
“Study hours predicted exam scores, b = 1.52, t(88) = 4.98, p < .001, R² = .22.”
Frequently asked questions
What does R² mean?
R² is the proportion of variance in the outcome explained by the predictor. An R² of .25 means the predictor explains 25% of the variance.
How do I interpret the slope?
The slope B is the expected change in Y for a one-unit increase in X. The standardized beta gives the same effect in standard deviation units.
What should the residual plot look like?
A random cloud around zero with no curve or funnel shape supports the linearity and constant-variance assumptions.
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