Can I Predict Outside The Observed X Range?

The calculator will evaluate the line, but extrapolation can be unreliable because the relationship may change beyond the data you observed.

What Does R Squared Mean?

For this one-predictor model, R² is the share of Y variation explained by the fitted linear relationship in the sample. It does not prove the model is causal or appropriate.

Linear Regression Calculator

Fit an ordinary least-squares line, inspect residuals and R², predict Y values and reveal the calculation steps.

Paired Data

Fit an ordinary least-squares line and inspect every residual.

X ValuesY Values

Separate values with commas, spaces, tabs or line breaks. Pairing follows position.

Load Paired CSV

Regression Plot

The fitted line and source observations share the same scale.

Residual Table

Residual equals observed Y minus predicted Y.

X	Observed Y	Predicted Y	Residual
1	2.1	2.016667	0.0833333
2	3.7	3.665476	0.0345238
3	5.2	5.314286	-0.1142857
4	7.1	6.963095	0.1369048
5	8.4	8.611905	-0.2119048
6	10.2	10.26071	-0.0607143
7	11.9	11.90952	-0.0095238
8	13.7	13.55833	0.1416667

Fitted Model

Least-Squares Equation

y = 1.6488095x + 0.36785714

Slope: 1.6488095
Intercept: 0.36785714
Pearson R: 0.99952438
R Squared: 0.99904898
Standard Error: 0.13459227

Predict Y For X

Predicted Y15.207143

Show Work

1. Mean X = 4.5; Mean Y = 7.7875.
2. Sum (x − mean X)² = 42.
3. Sum (x − mean X)(y − mean Y) = 69.25.
4. Slope = sum XY / sum XX; intercept = mean Y − slope × mean X.

Export Analysis

Check residual shape and subject-matter assumptions before using the model. A high R² does not make extrapolation safe.

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What Is the Linear Regression Calculator?

The Linear Regression Calculator fits the line that minimizes the sum of squared vertical residuals. It reports slope, intercept, Pearson r, R², residual standard error, a prediction for any X value and the observed-versus-predicted table.

How It Works

Paste paired X and Y values or load a paired CSV. Inspect the fitted line and residuals, enter an X value for a prediction, and turn on Show Work for the mean and deviation-sum steps.

When to Use It

Use it for education, exploratory modeling and transparent one-variable trend estimates.

Frequently Asked Questions

Can I Predict Outside The Observed X Range?: The calculator will evaluate the line, but extrapolation can be unreliable because the relationship may change beyond the data you observed.
What Does R Squared Mean?: For this one-predictor model, R² is the share of Y variation explained by the fitted linear relationship in the sample. It does not prove the model is causal or appropriate.

Found an issue? Send Feedback. See our data sources and update policy for tools that depend on changing information.