Positive Correlation
Positive correlation means that as one variable increases, the other variable tends to increase as well.
Definition
Positive correlation means two things tend to move in the same direction: when one goes up, the other tends to go up too. It exists when the correlation coefficient r is between 0 and +1, with a value near +1 indicating a strong positive linear relationship and near 0 a weak one; on a scatter plot, positively correlated data forms a cloud of points sloping upward from left to right. Formally, positive correlation corresponds to positive covariance: $\text{Cov}(X,Y) = E[XY] - E[X]E[Y] > 0$; for jointly normal $(X,Y)$, it means knowing $X > \mu_X$ increases the conditional expectation of $Y$ above $\mu_Y$, and partial correlation measures positive association between two variables while controlling for the effects of one or more additional variables.
Example
The more hours you study, the higher your test score tends to be, a positive correlation between study hours and test score, which on a scatter plot looks like dots drifting upward from left to right, like a hill. Height and weight of adult males have a strong positive correlation ($r \approx 0.7$), summarized by a line of best fit with a positive slope: taller men tend to weigh more. In a multiple regression, two predictors can be positively correlated with each other ($r = 0.8$) and both positively correlated with the response, and the partial correlation between each predictor and the response, controlling for the other, reveals their unique contribution, which may differ from the marginal correlation.
Key Insight
Strength matters as much as direction: a correlation of $r = 0.3$ is positive but weak, while $r = 0.9$ is positive and very strong, so always report the value, not just the direction. Multicollinearity in regression occurs when predictors are strongly positively (or negatively) correlated, inflating standard errors and making individual coefficient estimates unstable; variance inflation factors (VIF) quantify this problem.