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A negative correlation scatter plot is a scatter plot in which the points drift downward from left to right: as the value on the horizontal axis rises, the value on the vertical axis tends to fall. This guide shows how to recognise one, how the sign and size of Pearson’s r are worked out from the points themselves, and how to report the result.
What a scatter plot with negative correlation looks like
A scatter plot is a plot of the values of Y versus the corresponding values of X, with Y on the vertical axis and X on the horizontal axis (NIST/SEMATECH e-Handbook of Statistical Methods). In a scatter plot with negative correlation the cloud of points slopes down to the right: high values of one variable occur with low values of the other (OpenStax Introductory Statistics 2e, section 12.2). The NIST handbook labels the tightest version “Strong Linear (negative correlation)” and notes that a straight line comfortably fits through the data.
Strong versus weak negative correlation
The direction is the same in both cases; the tightness differs. OpenStax contrasts a pattern that “moves downward to the right, almost in a straight line” with a second pattern that still trends downward but whose points do not line up tightly. The first is a strong negative correlation, the second a weak one. Both are negative because the overall drift is downward.
The coefficient behind the plot: Pearson’s r
Pearson’s correlation coefficient r summarises a straight-line relationship in one number between −1 and +1. The sign gives the direction and the size gives the tightness: r near −1 means the points hug a downward-sloping line, and r near 0 means no linear pattern. See the correlation coefficient guide for the full range and verbal bands.
The formula is r = Σ(x−x̄)(y−ȳ) / √[Σ(x−x̄)² × Σ(y−ȳ)²], where x and y are paired observations, x̄ and ȳ are their means, and the sums run over all n pairs. The numerator adds up, for each point, the product of its horizontal deviation and its vertical deviation. That product is what produces the sign.
Draw the two mean lines through the plot and the points fall into four quadrants. Points in the upper-left (x below its mean, y above its mean) and the lower-right (x above, y below) give negative products. Points in the upper-right and lower-left give positive products. When most points sit in the upper-left and lower-right quadrants, the sum is negative and so is r.
Worked example with real arithmetic
Illustrative data, invented for teaching: an assay signal measured on eight consecutive days after a reagent vial was opened. It is not from a published study. Let x be days since opening and y the signal in arbitrary units.
| Day (x) | Signal (y) | x − 4.5 | y − 76.625 | Product | (x−x̄)² | (y−ȳ)² |
|---|---|---|---|---|---|---|
| 1 | 92 | −3.5 | 15.375 | −53.8125 | 12.25 | 236.3906 |
| 2 | 88 | −2.5 | 11.375 | −28.4375 | 6.25 | 129.3906 |
| 3 | 85 | −1.5 | 8.375 | −12.5625 | 2.25 | 70.1406 |
| 4 | 79 | −0.5 | 2.375 | −1.1875 | 0.25 | 5.6406 |
| 5 | 74 | 0.5 | −2.625 | −1.3125 | 0.25 | 6.8906 |
| 6 | 71 | 1.5 | −5.625 | −8.4375 | 2.25 | 31.6406 |
| 7 | 64 | 2.5 | −12.625 | −31.5625 | 6.25 | 159.3906 |
| 8 | 60 | 3.5 | −16.625 | −58.1875 | 12.25 | 276.3906 |
- Means: x̄ = 36 / 8 = 4.5 and ȳ = 613 / 8 = 76.625.
- Sum of products: −195.5. Every product is negative, so every point lies in the upper-left or lower-right quadrant.
- Sum of squares: Σ(x−x̄)² = 42 and Σ(y−ȳ)² = 915.875.
- r = −195.5 / √(42 × 915.875) = −195.5 / √38,466.75 = −195.5 / 196.13 = −0.997.
- The line of best fit has slope −195.5 / 42 = −4.65 and intercept 76.625 − (−4.65 × 4.5) = 97.57, so the signal falls by about 4.65 units per day.
- r² = 0.994, so about 99.4% of the variation in y is accounted for by the straight-line fit in these eight points.
Interpretation: reading guidance
| What you see | What it suggests |
|---|---|
| Points tightly along a downward line, r close to −1 | A strong negative linear relationship: higher x goes with lower y, consistently. |
| Downward drift with wide scatter, r moderately below 0 | A weak or moderate negative linear relationship; many points depart from the line. |
| No visible drift, r near 0 | No linear relationship; a non-linear pattern may still exist. |
| Downward but curved cloud | The relationship is negative but not linear, so r understates it and a straight line is the wrong summary. |
A negative correlation is not “bad”. It only describes direction. In the example above, a falling signal is simply what reagent decay looks like. Use the verbal bands for r cautiously and judge size against the field and the study; the scatterplot interpretation guide covers direction, form and strength in more depth.
Assumptions and common mistakes
- Linearity. Pearson’s r measures straight-line association. NIST lists “linearly related?” and “non-linearly related?” as separate questions a scatter plot answers, so look at the plot before trusting the number.
- Outliers. One extreme point can pull r toward or away from zero. Check the plot for points far from the cloud.
- Causation. A downward slope does not show that x lowers y. See correlation vs causation and spurious correlation.
- Sign confusion. r = −0.9 is a stronger relationship than r = +0.5. The sign is direction; the distance from zero is strength.
- Axis choice. Y is typically the response and X the suspected related variable, but r is the same either way round.
How to report a negative correlation
A common reporting pattern gives r with its degrees of freedom (n − 2) and the p value, keeping the minus sign. Check the style guide your journal or institution requires for details such as leading zeros. For the illustrative example: Signal fell with days since opening, r(6) = −0.997, p < 0.001. Here df = 8 − 2 = 6 and the t statistic is r√(n−2) / √(1−r²) = −30.5. Add a scatter plot with labelled axes and units, and a sentence on direction and size in plain words.
How to calculate it in Excel, R or Python
Using the same eight pairs, each returns r = −0.997.
Excel
=CORREL(A2:A9, B2:B9)With days in A2:A9 and signal in B2:B9. To draw the plot, select both columns and insert a Scatter chart.
R
x <- 1:8
y <- c(92, 88, 85, 79, 74, 71, 64, 60)
cor(x, y)
plot(x, y)Python
import numpy as np
import matplotlib.pyplot as plt
x = np.arange(1, 9)
y = np.array([92, 88, 85, 79, 74, 71, 64, 60])
print(np.corrcoef(x, y)[0, 1])
plt.scatter(x, y)
plt.show()More on plotting: scatter plots in Python and scatterplots in R.
FAQ
What does a negative correlation scatter plot show?
It shows points trending downward from left to right: high values of one variable pair with low values of the other.
Does negative correlation mean one variable causes the other to fall?
No. It describes how the two variables move together, not why. Other variables or chance can produce the same pattern.
Is negative correlation bad?
No. The sign is only a direction. A strong negative correlation is as informative as a strong positive one.
Can a scatter plot slope downward and r still be near zero?
Yes, if the downward drift is faint compared with the scatter, or if a few outliers distort the pattern. Check the plot and the value of r together.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods, Scatter Plot and Scatter Plot: Strong Linear (negative correlation) Relationship, checked 2026-10-29.
- OpenStax, Introductory Statistics 2e, 12.2 Scatter Plots, checked 2026-10-29.
