Scatter Plot Maker: Paste X and Y, Get r and R²

Q: How do I make a scatter diagram?

Measure both things on the same part or at the same moment (for example, the feed used and the roughness obtained), build two columns in Excel, one row per part, and paste them here. The suspected cause goes on the X axis and the effect on Y. With 25 to 30 pairs the picture is already reliable.

Q: How do I read a scatter diagram?

Look at the shape of the cloud. Rising from left to right: positive relationship. Falling: negative. A narrow band: strong relationship; a round cloud: weak or none. Then check the r written on the chart, the highlighted points far from the line and whether the group colors separate.

Q: What does r = 0.85 mean?

That the points line up well along a rising line: a strong positive relationship. Squared, R² = 72%, meaning about 72% of the part-to-part differences in Y move with X. The other 28% come from other causes or measurement error.

Q: Does a strong correlation prove that X causes Y?

No. Both may follow a third variable: in summer the cooling water temperature and the humidity both rise, for example. To confirm the cause, change X on purpose (a controlled test) and see whether Y responds as the line predicts.

Q: What is the group column for?

For stratification: color the points by machine, shift, supplier or tool. In the example, the worn insert sits above the new one for the same feed; without the colors that difference would be lost in the cloud.

Q: What is the quadrant method?

The classic paper reading of the diagram: draw the medians of X and Y and count the points in each quadrant. Many points in quadrants I and III indicate a positive relationship; in II and IV, negative. Turn on "Median lines" to see the count.

Q: When should I use full correlation or regression?

This page is for seeing and showing the chart. For several variables at once, a correlation matrix, tests and intervals, use Correlation; for a prediction equation with intervals or more than one X, use Regression. The buttons at the end of the page carry the same data.

Data

X and Y in two columns (paste from Excel, names in the first row); optional group column

Load .xlsx or .csv

Number format

See what was read

The 1st numeric column becomes the X axis (the cause you suspect) and the 2nd the Y axis (the effect). A text column with few values (machine, shift, supplier) colors the points by group; with many different values (part number, date) it becomes the point name. Decimal comma or point, tab or semicolon are accepted.

Chart

Fitted line

Colors by group

Median lines (quadrants)

Axes

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—Strength of the relationship

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Scatter diagram

Each point is a part or sample. Tap a point to see its row and values.

How to read: each point is an (X, Y) pair from the same part; X is horizontal, Y vertical. Points rising from left to right = positive relationship; falling = negative; a round cloud with no direction = no relationship. The closer to the line, the stronger the relationship (r near ±1). Marked diamonds are points far from the line: check what happened there.

Tap the chart to see the values.

Details: numbers by group and checks

N = pairs used; r = strength and direction (−1 to +1); 95% CI = likely range of the true r; R² = % of the variation in Y that follows the line; p-value < 0.05 = the relationship is unlikely to be chance; Spearman ρ = r computed from ranks only; S = typical distance of the points from the line, in Y units.

Next step

Take this page’s results to another calculator with the fields already filled in.

Full analysis: correlation, p-value and matrix →Regression: equation, CI and prediction →Y in collection order (run chart) →Histogram of Y →List other causes (Ishikawa) →

The calculation report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. The full report also includes the charts and interpretations, in color. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

r = Sxy/√(Sxx·Syy), with Sxy = Σ(x − x̄)(y − ȳ), Sxx = Σ(x − x̄)², Syy = Σ(y − ȳ)²; R² = r²

Least-squares line: b = Sxy/Sxx, a = ȳ − b·x̄; S = √[Σ(y − a − b·x)²/(N − 2)]

P-value: t = r·√[(N − 2)/(1 − r²)] with N − 2 degrees of freedom; 95% CI for r: tanh(atanh r ± 1.96/√(N − 3))

Standardized residual: eᵢ/(S·√(1 − hᵢ)), hᵢ = 1/N + (xᵢ − x̄)²/Sxx; Cook: Dᵢ = rᵢ²·hᵢ/[2(1 − hᵢ)]; Spearman ρ = r of the ranks (ties averaged)

Assumptions and limits

Strength scale used in the text: |r| < 0.2 very weak; 0.2 to 0.4 weak; 0.4 to 0.7 moderate; 0.7 to 0.9 strong; ≥ 0.9 very strong. It is a reading convention, not a test.
r measures only straight-line relationships. Curved relationships, mixed groups and extreme points can give a low r with a strong relationship, or a high r with no real one. Correlation does not show cause.
Median lines by the Minitab method (position (N + 1)p); points on a median are not counted in the quadrants. Above 6,000 points the chart draws a random sample; calculations use all of them.

Standards and technical documents

Ishikawa, K. Guide to Quality Control. Asian Productivity Organization, 1976 (cap. 6, diagrama de dispersão)
Montgomery, D. C. Introduction to Statistical Quality Control, 8th ed. Wiley, 2019, cap. 5
NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.3.26 Scatter Plot
ISO 7870-1:2019 Control charts — General guidelines (ferramentas básicas)

U.S. regulations

ISO 9001:2015, 9.1.3: analysis and evaluation
IATF 16949:2016, 10.2.3: problem solving

Frequently asked questions

How do I make a scatter diagram?

Measure both things on the same part or at the same moment (for example, the feed used and the roughness obtained), build two columns in Excel, one row per part, and paste them here. The suspected cause goes on the X axis and the effect on Y. With 25 to 30 pairs the picture is already reliable.

How do I read a scatter diagram?

Look at the shape of the cloud. Rising from left to right: positive relationship. Falling: negative. A narrow band: strong relationship; a round cloud: weak or none. Then check the r written on the chart, the highlighted points far from the line and whether the group colors separate.

What does r = 0.85 mean?

That the points line up well along a rising line: a strong positive relationship. Squared, R² = 72%, meaning about 72% of the part-to-part differences in Y move with X. The other 28% come from other causes or measurement error.

Does a strong correlation prove that X causes Y?

No. Both may follow a third variable: in summer the cooling water temperature and the humidity both rise, for example. To confirm the cause, change X on purpose (a controlled test) and see whether Y responds as the line predicts.

What is the group column for?

For stratification: color the points by machine, shift, supplier or tool. In the example, the worn insert sits above the new one for the same feed; without the colors that difference would be lost in the cloud.

What is the quadrant method?

The classic paper reading of the diagram: draw the medians of X and Y and count the points in each quadrant. Many points in quadrants I and III indicate a positive relationship; in II and IV, negative. Turn on "Median lines" to see the count.

When should I use full correlation or regression?

This page is for seeing and showing the chart. For several variables at once, a correlation matrix, tests and intervals, use Correlation; for a prediction equation with intervals or more than one X, use Regression. The buttons at the end of the page carry the same data.

Scatter diagram

Next step

Method, assumptions and references

Equations used

Assumptions and limits

Standards and technical documents

U.S. regulations

Frequently asked questions

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