Correlation_basicsrelatedtoanalytics.pptx

basic concepts and problems in correlation

1. Introduction to Correlation • Correlation measures the strength and direction of a linear relationship between two variables. • Denoted by 'r', known as the correlation coefficient. • Range: -1 ≤ r ≤ +1.

2. Types of Correlation • Positive correlation: As X increases, Y increases. • Negative correlation: As X increases, Y decreases. • Zero correlation: No relationship between X and Y.

3. Scatter Plots • A scatter plot visually represents correlation between two variables. • Tight clustering around a line indicates strong correlation.

4. Pearson’s Correlation Coefficient Formula: r = Σ[(X - X̄)(Y - Ȳ)] / √[Σ(X - X̄)² Σ(Y - Ȳ)²] • Measures linear relationship. • Sensitive to outliers.

5. Interpretation of r • r = +1 : Perfect positive correlation. • r = -1 : Perfect negative correlation. • r = 0 : No correlation. • 0.7 < |r| ≤ 1 → Strong correlation.

6. Example Problem Given data: X = [2, 4, 6, 8, 10], Y = [3, 7, 5, 11, 14] 1. Calculate X̄ and Ȳ. 2. Apply Pearson formula. 3. Compute r = 0.88 → strong positive correlation.

7. Applications of Correlation • Finance: Stock price movements. • Education: Study hours vs. marks. • Healthcare: Dosage vs. recovery rate.

8. Summary • Correlation shows direction and strength of linear relationship. • Visualized through scatter plots. • Pearson’s r quantifies correlation.