Calculator Inputs
Formula Used
Weighted regression fits a straight line while giving stronger influence to observations with larger weights.
- Objective: Minimize
Σ wᵢ (yᵢ - (b₀ + b₁xᵢ))² - Weighted mean of x:
x̄w = Σ(wᵢxᵢ) / Σwᵢ - Weighted mean of y:
ȳw = Σ(wᵢyᵢ) / Σwᵢ - Slope:
b₁ = Σ[wᵢ(xᵢ - x̄w)(yᵢ - ȳw)] / Σ[wᵢ(xᵢ - x̄w)²] - Intercept:
b₀ = ȳw - b₁x̄w - Prediction:
ŷ = b₀ + b₁x - Weighted R²:
1 - SSE / SST, whereSSE = Σ[wᵢ(yᵢ - ŷᵢ)²]andSST = Σ[wᵢ(yᵢ - ȳw)²].
In software development, weights often represent measurement reliability, sample confidence, request volume, or benchmark importance.
How to Use This Calculator
- Enter a dataset label, optional prediction x value, and preferred decimal precision.
- Add weighted observations in the table. Each row needs x and y. Weight is optional there and defaults to 1.
- Optionally paste extra rows in CSV or TSV format using
x,y,w. - Click Calculate Weighted Regression to compute the fitted line, metrics, prediction, and residual table.
- Review the Plotly chart to inspect weighted points and the regression line.
- Export the final summary and detailed rows using the CSV or PDF buttons.
Example Data Table
Sample benchmark-style observations you can test immediately.
| Row | X | Y | Weight | Scenario |
|---|---|---|---|---|
| 1 | 1 | 1.8 | 1.0 | Small input size, lower confidence |
| 2 | 2 | 3.9 | 2.0 | Repeated benchmark run |
| 3 | 3 | 6.1 | 1.5 | Moderate load sample |
| 4 | 4 | 8.0 | 3.0 | High-confidence measurement |
| 5 | 5 | 10.2 | 2.5 | Stable final benchmark |
FAQs
1. What does weighted regression do?
It fits a line to data while giving stronger influence to observations with larger weights. This is useful when some software measurements are more reliable, repeated more often, or represent higher-value traffic.
2. When should I use weights?
Use weights when observations have different confidence levels, noise levels, request counts, or business importance. For example, a benchmark averaged over many runs may deserve a larger weight than a single noisy run.
3. Is weighted regression the same as ordinary linear regression?
No. Ordinary regression treats every point equally. Weighted regression changes the fit so higher-weight points pull the line more strongly. If all weights are equal, both methods produce the same line.
4. What kind of software data works well here?
You can model latency versus payload size, memory use versus records processed, build time versus modules, defect rate versus test coverage, or any roughly linear relationship with meaningful observation weights.
5. What happens if every x value is identical?
The slope becomes undefined because there is no x variation. This calculator checks for that condition and stops, since a unique regression line cannot be estimated from constant x values.
6. How should I choose good weights?
Choose weights using a consistent rule. Common choices include sample count, confidence score, inverse variance, or measurement reliability. Avoid arbitrary weights unless you can explain how they represent trust or importance.
7. What does a low R-squared mean?
A low R-squared means the weighted line explains little of the weighted variation in y. Your relationship may be weak, non-linear, noisy, or driven by omitted variables.
8. Can I export the results for reports?
Yes. Use the CSV button for spreadsheets and the PDF button for report-friendly output. Both exports include summary metrics and the row-level regression details shown on the page.