Understanding the phrase which of the following is not a possible r value is a common need for students, data analysts, and anyone who interprets correlation results. At its core this question asks you to recognize the allowable range and meaning of the Pearson correlation coefficient (r), spot values that violate mathematical constraints, and avoid common interpretation mistakes when you present correlations to others.
A clear answer to which of the following is not a possible r value (short and precise)
The mathematical reason r must lie between -1 and 1
How to compute and check r so you don’t accept impossible answers
Practical interpretation guidance and common pitfalls to avoid
How to explain impossible r values to nontechnical stakeholders using communication best practices
A compact FAQ to lock in the main takeaways
In this post you will get:
Key short answer: Any number less than -1 or greater than 1 (for example, -1.5 or 1.2) is not a possible r value for Pearson’s correlation coefficient. The Pearson r always lies between -1 and 1 inclusive because it is a standardized covariance divided by the product of standard deviations LibreTexts/12:BivariateCorrelation/12.05:Interpretationofr-Values) and Dummies.
What does which of the following is not a possible r value mean and why does it matter
That phrasing usually appears in multiple-choice tests or quick data-check questions. It asks you to identify which candidate number cannot be the Pearson correlation coefficient for any real-world paired dataset.
It prevents accepting calculation errors or reporting impossible results.
Misstated correlations undermine credibility in reports and presentations.
Recognizing impossible values helps catch data problems (e.g., zero variance, computational mistakes) early.
Why it matters:
The technical reason is straightforward: Pearson’s r is computed as the covariance of two variables divided by the product of their standard deviations. Because covariance is bounded by the product of standard deviations (by the Cauchy–Schwarz inequality), r must lie in [-1, 1] freeCodeCamp and LibreTexts/12:BivariateCorrelation/12.05:Interpretationofr-Values).
Why is which of the following is not a possible r value a common test question
It tests whether students remember that r cannot exceed 1 in magnitude.
It reveals whether students confuse other statistics (e.g., R-squared, regression coefficients) with r.
It encourages students to check edge cases such as perfect correlation (r = ±1) and undefined correlation (e.g., when a variable has zero variance).
Educators use this prompt because it checks both conceptual understanding and attention to computation:
Multiple-choice distractors often include numbers like 0.95 (possible), -0.85 (possible), 1.2 (impossible), and -1 (possible). The correct pick is any value outside [-1, 1], such as 1.2 or -1.5.
How do you compute r so you can answer which of the following is not a possible r value
Knowing the formula helps you see why impossible values are indeed impossible.
r = sum [(xi - x̄)(yi - ȳ)] / sqrt( sum (xi - x̄)^2 * sum (yi - ȳ)^2 )
Pearson correlation coefficient r (sample version) formula:
This is the sample covariance divided by the product of sample standard deviations. Because the denominator scales covariance to a standardized measure, r cannot exceed 1 in absolute value freeCodeCamp and Wikipedia.
Data: x = [1, 2], y = [2, 4]
Covariance is positive and when divided by the product of standard deviations you get r = 1 (perfect positive linear relation).
If you attempted to produce r = 1.2 for any real data, you’d find that algebra or calculation must be wrong because the denominator cannot be smaller than the numerator required to boost r beyond 1.
Quick worked example (mini):
If either variable has zero variance (all x equal or all y equal), the denominator is zero and r is undefined. That’s a data-quality issue, not a correlation value.
When r cannot be computed:
What are common mistakes when answering which of the following is not a possible r value
Confusing r with R-squared or regression coefficients
R-squared (R^2) ranges 0 to 1 and is the square of r in simple linear regression; a value like 0.64 corresponds to r = ±0.8, but R^2 itself would never be negative. Don’t swap these concepts.
Forgetting sample vs population computations
Sample r estimates population correlation ρ; large samples give more stable r estimates. Small samples can produce noisy r values that are still within [-1, 1] but may be unreliable PMC article on statistical interpretation.
Believing rounding errors can justify impossible values
Computational mistakes or programming bugs can produce r values slightly > 1 (e.g., 1.0000002) because of floating-point error. Treat such tiny exceedances as numerical issues and re-check your code or use higher precision.
Reporting a correlation when variables are nonlinearly related
Strong nonlinear relationships can have r near 0; misinterpreting r=0 as “no relationship” is a mistake. r specifically measures linear association Dummies.
Not checking missing data or pairwise mismatches
Mismatched pairs (e.g., aligning the wrong rows) can produce bizarre r results that look mathematically possible but are substantively meaningless.
How should you explain which of the following is not a possible r value to a nontechnical audience
When presenting correlations to stakeholders, clarity matters. Use these steps adapted from communication best practices (the “Five Rs”) so your explanation lands and drives action Duxnotes on Five Rs and Cerkl on ROI communications.
Relevance: Start by saying why the correlation matters to their decision. Example: “This metric tells us whether changes in website visits tend to go along with sales.”
Right Message: State the key fact plainly: “Correlation r must be between -1 and 1. If you see numbers outside that range, we should re-check the calculation.”
Right Person: Tailor depth to your audience. For executives, keep it short: “Values outside -1 to 1 are impossible.” For analysts, show the formula and code check.
Right Time: Bring this up when results are reviewed, especially if numbers look inconsistent.
Right Way: Use a simple visual: a small scatterplot with lines showing perfect positive (r = 1), no linear (r ≈ 0), and perfect negative (r = -1). Explain that r scales covariance to a standard scale.
“Pearson’s r measures linear association on a scale from -1 (perfect negative) to +1 (perfect positive). Any number beyond that is a calculation error or data issue, so we’ll re-run the analysis if we see it.”
A short script you can use:
Cite the Five Rs framework if you want to justify communication choices to a team: Duxnotes and for tying correlation reporting to impact/ROI, see Cerkl.
When might you see a reported r value that appears impossible and what to do
Floating-point or rounding error in software output. Many languages report tiny overshoots; clip or round safely.
Incorrect formula implementation (e.g., using population formulas incorrectly with sample standard deviations).
Data preprocessing errors (e.g., mismatched pairs, unintended duplication).
Mislabeling: the number might not be Pearson r (maybe it’s a different statistic misnamed).
If a report shows r = 1.05 (for example), consider these possibilities:
Re-run the computation with a trusted library (e.g., statistical package functions).
Check for zero variance or constant columns.
Confirm pair alignment and missing-value handling.
If the overshoot is tiny (e.g., 1.0000000002), treat it as numerical noise, but document it.
Action checklist:
Software tip: Many statistical libraries provide built-in correlation functions that handle numerical stability. If you implement the formula yourself, include explicit checks to clip r into [-1, 1] after computation if the excess is within machine-epsilon.
How does sample size affect which of the following is not a possible r value and its interpretation
Precision: Small samples produce more variable r estimates; observed r may swing widely even while staying within bounds.
Significance: Whether an observed r differs meaningfully from 0 depends on sample size. A small r in a very large sample can be statistically significant but practically trivial PMC on statistical interpretation.
Sample size doesn’t change the mathematical bounds of r — it will always remain within [-1, 1]. However sample size matters for:
Report r with confidence intervals or p-values when relevant.
Emphasize effect size (magnitude) and practical importance, not just significance.
Practical guidance:
What are examples of impossible r values people commonly see in real life
r = 1.2 or r = -1.5 — impossible by definition; check arithmetic or software.
r = NaN or undefined — occurs when a variable has zero variance.
r slightly above 1 like 1.0000001 — likely floating-point rounding; clip to 1.
r = 2 in a published infographic — almost certainly a mislabel (maybe they reported a different metric like a slope or an index).
Examples you might encounter and why they’re impossible:
When you read papers or dashboards, a quick sanity check is: 1) is r within [-1, 1]? 2) Does the magnitude make sense given the scatterplot? 3) Are there data processing issues?
What Are the Most Common Questions About which of the following is not a possible r value
Q: Can r be greater than 1 or less than -1
A: No. Pearson r always lies between -1 and 1 inclusive; outside values indicate error.
Q: Can rounding make r slightly above 1
A: Yes small numerical overshoots happen; treat tiny exceedances as machine precision issues.
Q: Is r undefined for constant variables
A: Yes. If one variable has zero variance, r is undefined because you can’t divide by zero.
Q: Does r=0 mean no relationship at all
A: No. r=0 means no linear relationship; nonlinear associations can still exist.
Q: Is R-squared the same as r
A: No. R-squared is r^2 in simple linear cases; it’s always nonnegative and interpreted differently.
Q: Should I trust very high r in small samples
A: Be cautious—small samples can show extreme r by chance; report confidence intervals.
(Each Q/A above is designed to be concise and focused on common confusions.)
Quick checklist to answer which of the following is not a possible r value on exams or in reports
If candidate value < -1 or > 1 → mark as not possible.
If candidate value equals -1, 0, or 1 → possible (interpret as perfect negative, none linear, perfect positive respectively).
If a reported value slightly exceeds 1 by a tiny margin → treat as numeric error; re-check calculation.
If r undefined → suspect zero variance in a variable.
When in doubt, plot the data. A scatterplot reveals whether a reported r is plausible.
Further reading and trusted references
For an accessible guide to interpreting r values and practical rules of thumb, see Dummies on interpreting correlation coefficients.
For the derivation and interpretation of r and why it’s bounded, see the open-statistics text at LibreTexts on r interpretation/12:BivariateCorrelation/12.05:Interpretationofr-Values).
For beginner-friendly explanations and implementation notes, see freeCodeCamp’s article on correlation coefficient r.
For guidance on communicating statistics and tying results to ROI, explore content on effective communication frameworks like the Five Rs Duxnotes and ROI-focused communication Cerkl.
Final takeaway: which of the following is not a possible r value? Any number outside the closed interval [-1, 1] — and spotting such a value quickly saves time, prevents reporting errors, and helps you tell a clearer story with your data.
