Formula Used:
Pearson Correlation Coefficient (r):
r = [ n(Σxy) - (Σx)(Σy) ] / √[ (n(Σx²) - (Σx)²) * (n(Σy²) - (Σy)²) ]
Theory & Interpretation:
The Pearson Correlation Coefficient (r) is a measure of the strength and direction of a linear relationship between two continuous variables. Its value ranges from -1 to +1.
- Direction of Relationship:
- Positive (r > 0): As one variable increases, the other variable tends to increase.
- Negative (r < 0): As one variable increases, the other variable tends to decrease.
- No Linear Relationship (r ≈ 0): There is no discernible linear trend between the variables.
- Strength of Relationship (General Guide):
- 0.8 to 1.0 (or -0.8 to -1.0): Very Strong
- 0.6 to 0.8 (or -0.6 to -0.8): Strong
- 0.4 to 0.6 (or -0.4 to -0.6): Moderate
- 0.2 to 0.4 (or -0.2 to -0.4): Weak
- 0.0 to 0.2 (or -0.0 to -0.2): Very Weak or No relationship
- Coefficient of Determination (R²): This is simply r². It represents the proportion of the variance in one variable that is predictable from the other variable. For example, an r of 0.8 gives an R² of 0.64, meaning 64% of the variability in Y can be "explained" by the variability in X.
Crucial Note: Correlation does NOT imply causation! Just because two variables are strongly correlated does not mean that one causes the other. There could be a third, unobserved variable (a confounding variable) influencing both.
Step-by-step Calculation:
