Calculator Inputs
Example Data Table
| Study hours | Score | Expected use |
|---|---|---|
| 1 | 2.1 | Low input point |
| 4 | 4.2 | Middle trend point |
| 8 | 8.1 | High input point |
Formula Used
The calculator uses ordinary least squares for the standard model.
Slope: b = Σ((x - x̄)(y - ȳ)) / Σ((x - x̄)²)
Intercept: a = ȳ - bx̄
Prediction: ŷ = a + bx
Correlation: r = Σ((x - x̄)(y - ȳ)) / √(Σ(x - x̄)² Σ(y - ȳ)²)
R squared: R² = 1 - SSE / SST
How to Use This Calculator
- Paste two numeric columns into the data box.
- Enter one x value for prediction.
- Select the fit mode, interval, and decimal places.
- Press Calculate Regression.
- Review the equation, graph, residuals, and fit statistics.
- Use CSV or PDF to download your results.
Linear Regression Graph Guide
Linear regression is a simple way to study paired numbers. It checks how one value changes when another value moves. The calculator reads your x and y values. It then finds the best straight line through the pattern. That line is useful for trend checks, forecasts, and quick model reviews.
The graph makes the result easier to read. Each point shows one observation. The fitted line shows the average direction of the data. Points close to the line suggest a strong fit. Points far from the line suggest noise, outliers, or missing causes. Use the residual table to see those gaps clearly.
The slope tells you the expected y change for one x unit. A positive slope means y tends to rise. A negative slope means y tends to fall. The intercept estimates y when x is zero. This value may not be practical if zero is outside your data range. Always compare the output with real subject knowledge.
Correlation measures direction and strength. R squared shows how much variation is explained by the line. A high value can be helpful. It does not prove a cause. A low value does not always make the model useless. Some fields have noisy data, yet trends still support decisions.
Prediction is best inside the observed x range. Outside that range, the estimate becomes less safe. This is called extrapolation. Check residuals before trusting any forecast. A curved residual pattern may mean a straight line is not enough. Try another model when the pattern is clearly curved.
Clean data improves results. Remove duplicate rows only when they are mistakes. Keep real repeated readings. Use the same units for every row. Check decimal separators before pasting. Extreme outliers deserve review, not automatic removal. They may show errors, special cases, or important events. Review sample rows first, then paste your own values after removing headings, blank lines, labels, and notes that are not numeric.
Use exported files for records. The CSV file supports spreadsheet checks. The PDF file gives a quick report. Save the graph by using your browser tools if needed. For stronger analysis, compare the output with domain rules. A calculator is a guide, not a final judge. Good decisions still need context.
FAQs
What does a linear regression graph show?
It shows your data points and the fitted straight line. The line summarizes the average relationship between x and y values.
What is the slope in regression?
The slope is the expected change in y for each one unit increase in x. It can be positive, negative, or zero.
What does the intercept mean?
The intercept is the predicted y value when x equals zero. It is useful only when zero makes sense for your data.
What is R squared?
R squared estimates how much y variation is explained by the fitted line. Higher values usually mean a closer linear fit.
Can I use this calculator for forecasting?
Yes, but forecasts are safer inside the observed x range. Predictions far outside the data range can be unreliable.
What are residuals?
Residuals are actual y values minus predicted y values. They show how far each point sits from the fitted line.
Should I remove outliers?
Remove outliers only when they are confirmed errors. Real unusual points may hold important information about the process.
What data format should I paste?
Paste one x,y pair per line. You may use commas, spaces, tabs, or semicolons between the two numbers.