Interactive Tools/Regression Diagnostics Explorer

Regression & Correlation

Regression Diagnostics Explorer

Paste a data set and see not just the fitted line, but the diagnostics that reveal whether any single point is quietly controlling the result.

Your data

One pair per line as x, y. 6 points read.

ŷ = 5.178 + 0.3677x, R² = 0.3009

Fit (red = outlined = high leverage)

Residuals vs. fitted

x	y	Residual	Leverage	Cook's D
1	3	-2.546	0.3247	0.3792
2	5	-0.914	0.2473	0.0299
3	6	-0.282	0.1957	0.002
4	9	2.351	0.1699	0.1119
5	10	2.983	0.1699	0.1802
12	8	-1.591	0.8925	16.0547

Rows shaded amber have leverage above 2p/n = 0.667; rows shaded red have Cook's distance above 1, a common threshold for an influential point. Try removing the last point in the default example and watch the slope, R², and every diagnostic change, exactly the effect described in leverage, outliers and Cook's distance.

How to use this tool

Paste your (x, y) pairs, one per line.
The left chart shows the fit; points outlined in black have high leverage, and points filled red have a Cook's distance above 1.
The right chart plots residuals against fitted values — a random-looking scatter around zero is what a good fit looks like.
Check the table for the exact leverage and Cook's distance of every point, and try editing or removing a point to see how much the fit changes.

Formula Reference

Leverage

h_i = 1/n + (x_i - x̄)² / Sxx

Cook's distance

D_i = [e_i² / (p·MSE)] × [h_i / (1 - h_i)²]

Rule of thumb thresholds

leverage above 2p/n, Cook's D above 1 or above 4/n

ArticleLeverage, Outliers, and Cook's Distance ArticleSimple Linear Regression ToolScatter Plot & Correlation Visualizer CalcLinear Regression Calculator CalcMultiple Regression Calculator GlossaryGlossary: Influential Point

Frequently Asked Questions

What is the difference between this and the Scatter Plot Visualizer?+

The scatter tool shows the correlation and the fitted line. This tool goes further, showing the residual pattern and flagging exactly which points have unusual influence over the fit, using the same leverage and Cook's distance formulas as the influential-points article.

Why can a point have high leverage but a small residual?+

A point far out in x pulls the line toward itself, which can shrink its own residual even while it distorts the fit for everyone else. That is exactly why leverage and Cook's distance are needed alongside a plain residual plot.

What should I do if a point is flagged as influential?+

Check it is not a data-entry error first. If it is genuine, consider reporting the analysis with and without it, since a conclusion that depends entirely on one point is fragile.

What does a good residuals-vs-fitted plot look like?+

A random scatter of points around the zero line, with no funnel shape (which would suggest changing variance) and no curve (which would suggest a straight line is the wrong model).

Residual

Leverage

Cook's D

-2.546

0.3247

0.3792

-0.914

0.2473

0.0299

-0.282

0.1957

0.002

2.351

0.1699

0.1119

2.983

0.1699

0.1802

-1.591

0.8925

16.0547

How to use this tool

Paste your (x, y) pairs, one per line.

The left chart shows the fit; points outlined in black have high leverage, and points filled red have a Cook's distance above 1.

The right chart plots residuals against fitted values — a random-looking scatter around zero is what a good fit looks like.

Check the table for the exact leverage and Cook's distance of every point, and try editing or removing a point to see how much the fit changes.