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Compute Pearson’s r between two lists of numbers.
Results update as you type.
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Pearson’s correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables, ranging from −1 (perfect negative) through 0 (no linear relationship) to +1 (perfect positive). It is found by dividing the covariance of x and y by the product of their standard deviations, which standardises the result into that fixed −1 to +1 range. It needs at least two pairs, and the result is undefined if either variable never changes. It needs at least two pairs, and the result is undefined if either variable never changes. It needs at least two pairs, and the result is plotted with its best-fit line. The calculator returns r, the coefficient of determination r², the covariance, and the least-squares regression line (slope and intercept), plus a plain-English reading of the strength, and plots the data with its best-fit line.Worked example: for x = 1, 2, 3, 4, 5 and y = 2, 4, 5, 4, 6 the points trend upward together, giving r ≈ 0.85 — a strong positive correlation — and r² ≈ 0.73, meaning about 73% of the variation in y.Worked example: for x = 1, 2, 3, 4, 5 and y = 2, 4, 5, 4, 6 the points trend upward together, giving r ≈ 0.85 — a strong positive correlation — and r² ≈ 0.73, meaning about 73% of the variation in y is explained by a straight-line relationship with x.Worked example: for x = 1, 2, 3, 4, 5 and y = 2, 4, 5, 6, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 2
Tambayoyi da ake yi da yawa
What does the correlation coefficient tell me?
Yana nuna yadda mawallafi biyu ke motsa tare a cikin wani layin daidai. Kimar kusa da +1 ko -1 na nuna dangantaka mai ƙarfi, yayin da kimar kusa da 0 na nuna dangantaka mai ƙaranci ko kuma babu. Alamar tana nuna hanya na dangantaka.
Shin, ma'ana dangantaka tanã nufin dalili?
No. A high correlation shows two variables move together but not that one causes the other. A hidden third factor, or pure coincidence, can create a strong correlation with no causal link.
Mẽne ne R²?
R² shine kwance na ma'aunin dangantaka. Shi ne adadin bambance-bambancen cikin y da aka bayyana ta hanyar dangantaka mai layin-da-layin da x - r na 0.8 yana ba da R² na 0.64, yana nufin 64% na bambance-bambancen an yi la'akari da shi.
Me ya ke da alaƙa mai ƙarfi?
As a rough guide, an absolute r below 0.3 is weak, around 0.3 to 0.5 moderate, 0.5 to 0.7 moderate-to-strong and above 0.7 strong. This calculator labels the strength for you, but sensible cutoffs vary by field.
What does a negative correlation mean?
A negative r means the variables move in opposite directions: as one rises the other tends to fall. An r of −0.9 is just as strong a linear relationship as +0.9, only reversed in direction.
Me ya sa akwai bambanci tsakanin dangantaka da bambanci?
Covariance measures how two variables vary together but its size depends on their units, so it is hard to interpret. Pearson’s r is the covariance divided by the two standard deviations, which rescales it to a unit-free −1 to +1 range.
Ta yaya layin dawo da yake danganta da dangantaka?
The least-squares regression line is the straight line that best fits the points, and its slope shares its sign with r. The correlation tells you how tightly the points hug that line, while r² gives the share of variation the line explains.
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[Translation temporarily unavailable. Please try again.] Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. [Translation temporarily unavailable. Please try again.] →
Endpoint
GET https://calculator.free/api/v1/correlation-coefficient/curl
curl "https://calculator.free/api/v1/correlation-coefficient/?x=1, 2, 3, 4, 5&y=2, 4, 5, 4, 6"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/correlation-coefficient/?" + new URLSearchParams({
"x": "1, 2, 3, 4, 5",
"y": "2, 4, 5, 4, 6"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.