Same data. Two different questions. Correlation asks whether variables move together; regression asks how one variable predicts another.
Use correlation to describe association strength. Use regression when you need a prediction equation, a slope in real units, or control variables.
Your question is descriptive: whether two variables move together and how strongly. A correlation coefficient gives exactly that answer without forcing a predictor/outcome direction.
Best for: Reporting r, direction, strength, p-value, and confidence interval.
The methods overlap mathematically in simple linear cases, but they answer different research questions.
Are X and Y related, and how strong is that relationship?
How does X predict Y, and how much can Y be predicted?
A single coefficient: r, from -1 to +1
An equation: y-hat = b0 + b1x
Symmetric. Swapping X and Y gives the same r.
Directional. Swapping X and Y gives a different equation.
No direction is assumed.
X is treated as the predictor and Y as the outcome.
Cannot predict a concrete Y value.
Can produce a predicted value for Y.
Simple correlation cannot control third variables.
Multiple regression can control confounders.
Usually two continuous or ordinal variables.
Y is continuous; X can be continuous or categorical.
r, r squared, p-value, confidence interval
b coefficients, R squared, F statistic, t tests, p-values
Exploratory analysis and correlation matrices
Prediction, effect-size estimation, and adjusted models
Twenty A&E patients. X is age. Y is ln(urea). Both analyses are correct, but they give different kinds of information.
Pearson correlation: r = 0.57
p-value: p = 0.009
95% CI: [0.16, 0.80]
Interpretation:
There is a moderate positive correlation between age
and ln(urea) in A&E patients (r = .57, p = .009).
Older patients tend to have higher urea levels.Regression equation: ln(urea) = 0.88 + 0.017 x age
R² = 0.325
F(1, 18) = 8.67, p = 0.009
Interpretation:
For each additional year of age, ln(urea) increases
by 0.017 units on average. A 70-year-old patient
is predicted to have ln(urea) = 0.88 + 0.017 x 70 = 2.07,
or urea ≈ 7.9 mmol/L.Correlation has no predictor and no outcome: r(X, Y) equals r(Y, X). Regression is directional. The line for predicting urea from age is not the same as the line for predicting age from urea, because each line minimizes a different kind of error.
The cleanest choice usually follows from the wording of the research question.
You have a dataset with 10 variables and want to know which pairs are related before modeling.
It quickly scans every variable pair and shows which relationships deserve deeper study.
You want to check whether two blood pressure monitors give readings that move together.
You are comparing consistency between two measures, not predicting one from the other.
You want to predict a patient's urea level from their age.
Only the regression equation gives a concrete predicted value.
You want to know how much ln(urea) rises for every additional year of age.
The slope b1 directly reports change in Y per 1-unit increase in X.
You want to know whether exercise predicts blood pressure after age, BMI, and smoking are controlled.
Simple correlation cannot remove the influence of third variables.
You assigned drug dosages of 0, 10, 20, and 50 mg, then measured response.
When X is experimentally set, treating it as a predictor is the scientifically correct framing.
Correlation and simple linear regression are closely related. They are not the same method, but they share algebra in the one-predictor case.
The slope depends on units. If you change the scale of X or Y, the slope changes, but stays the same.
That identity holds for one predictor. In multiple regression, R² is still the explained variance, but it is no longer just the square of one correlation.
Regression is not just correlation with a line attached. It asks for a different set of assumptions about residuals and prediction.
Required for Pearson correlation
Required for linear regression
X is part of the bivariate normal assumption
X does not need to be normally distributed
Y is part of the bivariate normal assumption
Residuals should be approximately normal, not necessarily Y itself
Not usually stated as a separate assumption
Residual variance should be roughly constant
Observations should be independent
Observations should be independent
X is usually an observed measurement
X can be observed, categorical, or experimentally manipulated
These errors are common because the two methods are mathematically related, which makes them easy to blur together.
r = .85 between ice cream sales and drowning deaths proves ice cream causes drowning.
Correlation measures association, not causation. A third variable such as summer temperature may drive both.
I ran a regression even though I had no scientific reason to choose a predictor.
If you do not have a predictor/outcome framework, correlation is the cleaner first step.
r = .70 means Y increases by 0.70 units for every 1-unit increase in X.
That is the slope b1. r is unit-free; the slope depends on the measurement scale.
A simple correlation is enough even when age, BMI, or smoking could distort the result.
Use multiple regression or partial correlation when you need to control for a third variable.
Report correlation when the analysis is symmetric. Report regression when age, dose, exposure, or another predictor is used to estimate an outcome.
A Pearson correlation was conducted to assess the relationship between age and ln(urea). There was a moderate positive correlation between the two variables, r(18) = .57, p = .009, 95% CI [.16, .80].A simple linear regression was performed to examine whether age predicted ln(urea). Age significantly predicted ln(urea), b = .017, t(18) = 2.94, p = .009. Age accounted for 32.5% of the variance in ln(urea), R² = .325, F(1, 18) = 8.67, p = .009.A quick reference for readers who only need the method choice, not the full derivation.
Correlation measures how strongly two variables move together. Regression models how one variable predicts another and can produce a prediction equation.
Yes. Correlation is complete on its own when your goal is association, not prediction or control of other variables.
Usually for simple linear relationships, yes. In simple linear regression, R² equals r². But a curved relationship can still make r look misleading.
Regression provides more information, but it also requires a directional modeling choice and more assumptions. Correlation is simpler and symmetric.
Use partial correlation when you want to measure association after removing a third variable without building a full predictive model.
Once you know which method fits, move into the calculation or interpretation page that matches your task.