Enter Regression Data
Paste comma-separated, space-separated, or line-by-line numeric values. The result will appear above this form after submission.
Example Data Table
Use this sample to test the calculator quickly. It produces a strong positive linear relationship with slight residual variation.
| Observation | X | Y |
|---|---|---|
| 1 | 1 | 2.1 |
| 2 | 2 | 3.9 |
| 3 | 3 | 6.2 |
| 4 | 4 | 7.8 |
| 5 | 5 | 10.1 |
| 6 | 6 | 11.9 |
Formula Used
The calculator solves a simple linear regression model:
ŷ = b0 + b1x
Slope:
b1 = Σ[(xi - x̄)(yi - ȳ)] / Σ[(xi - x̄)2]
Intercept:
b0 = ȳ - b1x̄
Coefficient of Determination:
R2 = SSR / SST
Residual Error:
SSE = Σ(yi - ŷi)2
Standard Error of Estimate:
RMSE = √(SSE / (n - 2))
Prediction Equation:
For any new X value, predicted Y = b0 + b1X
How to Use This Calculator
- Enter all X values in the first box.
- Enter all matching Y values in the second box.
- Keep both lists in the same order and length.
- Optionally add future X values for predictions.
- Select the confidence level and decimal precision.
- Press Solve Linear Regression.
- Review coefficients, R², ANOVA, residuals, and prediction intervals.
- Use the CSV or PDF buttons to export results.
Frequently Asked Questions
1) What data format can I paste into the inputs?
You can paste comma-separated values, values on separate lines, or values separated by spaces. Every X value must have one matching Y value.
2) What is the minimum number of points needed?
Use at least three paired observations. Two points create a line, but they do not provide enough degrees of freedom for useful error estimates.
3) Can this calculator predict future Y values?
Yes. Enter new X values in the prediction box, and the tool returns predicted Y values with mean confidence intervals and wider prediction intervals.
4) What does R² tell me?
R² shows how much variation in Y is explained by X. Higher values indicate a stronger linear fit, but not necessarily causation.
5) What is the difference between confidence and prediction intervals?
A confidence interval estimates the likely range for the average response at a given X. A prediction interval estimates the likely range for one new observation.
6) Can outliers change the result a lot?
Yes. A single extreme point can shift slope, intercept, and fit measures. Always inspect residuals and the chart before trusting conclusions.
7) Why does the calculator show coefficient significance?
It compares each coefficient’s t statistic with the selected confidence threshold. That helps you judge whether the estimated effect is meaningfully different from zero.
8) When should I avoid simple linear regression?
Avoid it when the pattern is clearly curved, errors vary wildly, observations depend on each other, or important predictors are missing from the model.