Perfect Correlation Calculator

Correlation Formula:

\[ r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}} \]

Correlation Coefficient (r):

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1. What Is Correlation?

Correlation measures the strength and direction of the linear relationship between two variables. It ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no linear relationship.

2. How Does The Calculator Work?

The calculator uses Pearson's correlation formula:

\[ r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}} \]

Where:

\( x_i, y_i \) — Individual data points
\( \bar{x}, \bar{y} \) — Means of x and y values
\( \sum \) — Summation of all values

Explanation: The formula calculates how much two variables change together relative to how much they vary individually.

3. Interpreting Correlation Values

Details:

+1.0: Perfect positive correlation
+0.7 to +0.9: Strong positive correlation
+0.4 to +0.6: Moderate positive correlation
+0.1 to +0.3: Weak positive correlation
0: No correlation
-0.1 to -0.3: Weak negative correlation
-0.4 to -0.6: Moderate negative correlation
-0.7 to -0.9: Strong negative correlation
-1.0: Perfect negative correlation

4. Using The Calculator

Tips: Enter comma-separated values for both X and Y variables. Ensure both lists have the same number of values. The calculator will compute the Pearson correlation coefficient.

5. Frequently Asked Questions (FAQ)

Q1: What does perfect correlation mean?
A: Perfect correlation (r = ±1) means all data points lie exactly on a straight line, indicating a perfect linear relationship.

Q2: Does correlation imply causation?
A: No, correlation only measures association, not causation. Two variables can be correlated without one causing the other.

Q3: What's the difference between correlation and regression?
A: Correlation measures the strength of relationship, while regression models the relationship to make predictions.

Q4: Can correlation detect non-linear relationships?
A: No, Pearson correlation only measures linear relationships. Non-linear relationships may have correlation near zero.

Q5: What sample size is needed for reliable correlation?
A: Generally, larger samples provide more reliable estimates. Minimum of 30 pairs is often recommended for stable results.