Coefficient Calculator
Calculate correlation coefficient (r), coefficient of determination (R^2), and coefficient of variation.
Enter Data Sets
Enter equal numbers of X and Y values
Data Points (5 pairs)
| i | X | Y |
|---|---|---|
| 1 | 1 | 2 |
| 2 | 2 | 4 |
| 3 | 3 | 5 |
| 4 | 4 | 4 |
| 5 | 5 | 5 |
Coefficient Formulas
Pearson Correlation (r)
r = Sum((xi-x)(yi-y)) / sqrt(Sum(xi-x)^2 x Sum(yi-y)^2)
Coefficient of Determination
R^2 = r^2
Coefficient of Variation
CV = (s / |x|) x 100%
Correlation Coefficient (r)
0.774597
Positive Strong Correlation
rCorrelation (r)
0.774597
R^2R-Squared (R^2)
60.00%
CVxCV of X
47.14%
CVyCV of Y
27.39%
Linear Regression
Best Fit Line
y = 0.6000x + 2.2000
Slope (m)
0.600000
Y-Intercept (b)
2.200000
Descriptive Statistics
X Mean
3.0000
Y Mean
4.0000
X Std Dev
1.4142
Y Std Dev
1.0954
Interpreting Coefficients
Correlation (r)
- r = 1: Perfect positive
- r = -1: Perfect negative
- r = 0: No correlation
R-Squared
Represents the proportion of variance in Y explained by X. A value of 0.8 means 80% of variance is explained.
CV (Variation)
Measures relative variability. Lower CV indicates more consistent data.