Correlation
Correlation measures the strength and direction of the relationship between two variables. It helps to understand how changes in one variable are associated with changes in another.
Meaning and Definition: Correlation describes the degree to which two variables move in relation to each other. Values range from -1 to +1:
+1: Perfect positive correlation.
0: No correlation.
-1: Perfect negative correlation.
Use of Correlation: Commonly used in statistics, economics, and science to identify relationships between variables and make predictions.
Covariance: Measures the extent to which two variables change together. It's the raw form of correlation but lacks standardization.
Scatter Diagram: A graphical representation where data points are plotted to visualize the relationship between two variables.
Types of Correlation:
Positive: Both variables increase or decrease together.
Negative: One variable increases while the other decreases.
No Correlation: No apparent relationship between the variables.
Karl Pearson’s Correlation Coefficient: A mathematical formula to measure linear correlation. It’s sensitive to outliers and assumes the relationship is linear.
Spearman’s Rank Correlation Coefficient: Measures the relationship between two ranked variables, useful for non-linear data.
Probable Error: An indicator of the reliability of the correlation coefficient. It provides a range within which the true correlation likely falls.
Regression
Regression analysis helps understand the relationship between dependent (response) and independent (predictor) variables and predicts the value of one variable based on another.
Meaning and Utility:
Regression predicts the outcome (dependent variable) based on the predictor (independent variable).
It’s widely used in forecasting, trend analysis, and decision-making.
Comparison Between Correlation and Regression:
Correlation: Measures the strength and direction of a relationship.
Regression: Explains the nature of the relationship and makes predictions.
Correlation is symmetric, while regression is not.
Regression Lines:
X on Y: Predicting X based on Y.
Y on X: Predicting Y based on X.
Regression Equations: Mathematical equations representing regression lines. Examples:
𝑌=𝑎+𝑏𝑋
(where 𝑎 is the intercept and 𝑏 is the slope).
𝑋=𝑐+𝑑𝑌
Regression Coefficients: Indicate the rate of change in the dependent variable for a unit change in the independent variable. These coefficients are essential for understanding the strength and direction of the relationship.
