Pearson Correlation Calculator
Calculate Pearson r correlation coefficient, R-squared, and the t-statistic for significance testing from 5 x-y data pairs.
Results
What is it?
The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two continuous variables. It ranges from -1 (perfect negative) to +1 (perfect positive), with 0 indicating no linear association. R-squared (r^2) represents the proportion of variance in Y explained by X.
How to use
Enter 5 pairs of (X, Y) data points. The calculator computes r using the formula: r = (n*sumXY - sumX*sumY) / sqrt((n*sumX^2 - sumX^2)(n*sumY^2 - sumY^2)). The t-statistic (t = r*sqrt(n-2)/sqrt(1-r^2)) can be compared to a t-table with df = n-2 = 3 for these 5 pairs.
Example scenario
Data: (2,4), (4,6), (5,5), (6,8), (8,9). sumX=25, sumY=32, sumXY=183, sumX2=145, sumY2=222. numerator = 5x183 - 25x32 = 915 - 800 = 115. denominator = sqrt((5x145 - 625)(5x222 - 1024)) = sqrt(100x86) = sqrt(8600) = 92.74. r = 115/92.74 = 0.9390. R^2 = 0.882 (88% of variance explained). t = 0.939*sqrt(3)/sqrt(1-0.882) = 2.994, df=3.
Pro tip
Pearson r interpretation: |r| < 0.1 = negligible, 0.1-0.3 = weak, 0.3-0.5 = moderate, 0.5-0.7 = strong, 0.7-0.9 = very strong, >0.9 = near-perfect (Cohen, 1988). Critical t values for df=3 (5 pairs): p<0.05 -> |t|>3.182; p<0.01 -> |t|>5.841. Pearson r assumes: (1) linear relationship, (2) bivariate normality, (3) no outliers. For non-normal or ordinal data, use Spearman rho instead. Correlation does NOT imply causation.