Analyze robust trends using pairwise slope medians. Import points, review fits, and inspect residual summaries. Download clean reports and plots for validation workflows today.
| x | y | Comment |
|---|---|---|
| 1 | 2 | Starting observation |
| 2 | 3 | Moderate increase |
| 3 | 5 | Higher response |
| 4 | 4 | Small deviation |
| 5 | 6 | Trend continues |
| 6 | 8 | Upper range point |
The Theil-Sen slope estimator computes every pairwise slope between distinct x values:
sij = (yj - yi) / (xj - xi)
The final slope estimate is the median of all valid pairwise slopes:
b1 = median(sij)
The intercept is estimated from the median of pointwise intercepts:
b0 = median(yi - b1xi)
The fitted line is then:
ŷ = b0 + b1x
This method is preferred when data may include outliers because the median is less sensitive than least squares averaging.
It estimates the central slope of a linear trend by taking the median of slopes formed from all valid point pairs. This makes the estimate resistant to unusual observations.
Ordinary least squares can shift strongly when outliers exist. The Theil-Sen method usually changes less because medians are more stable than means under contamination.
Yes, but pairwise slopes with identical x values are skipped because division by zero is undefined. Other valid pairs are still used.
It reports the median intercept computed as y minus slope times x for each point. This pairs naturally with the median slope estimate.
No. It summarizes the central monotonic linear tendency in noisy data. Strong curvature can still reduce fit quality, so inspect residuals and the plot.
MAE shows average absolute error. RMSE gives more weight to larger residuals. Together they help assess how close the fitted line stays to observed values.
Yes. The chart displays the original scatter points and the fitted line derived from the computed Theil-Sen slope and intercept.
It is useful in environmental, financial, engineering, and scientific datasets where a few abnormal observations could distort a standard regression line.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.