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Correlation
Correlation measures the strength and direction of a linear relationship between two variables. It helps us understand how changes in one variable relate to changes in another. The correlation coefficient, ranging from -1 to 1, provides insights into the nature of the association. Remember, correlation does not imply causation; it simply quantifies the degree of connection.
\[r = \frac{\sum_{i=1}^{n}(X_i - \bar{X})(Y_i - \bar{Y})}{\sqrt{\sum_{i=1}^{n}(X_i - \bar{X})^2} \sqrt{\sum_{i=1}^{n}(Y_i - \bar{Y})^2}}\]- Correlation measures the statistical relationship between two variables.
- It indicates the strength and direction of a linear relationship between them.
- Correlation coefficients range from -1 to 1, where -1 represents a perfect negative correlation, 1 represents a perfect positive correlation, and 0 indicates no correlation.
Regression
Regression takes us a step further by modeling the relationship between a dependent variable and one or more independent variables. The resulting equation represents the best-fit line or curve, enabling us to predict the dependent variable’s value based on given independent variables. While correlation provides insights into association, regression equips us with a predictive tool.
\[Y = b_0 + b_1X + \varepsilon\]- Regression is a statistical method that analyzes the relationship between a dependent variable and one or more independent variables.
- It helps in predicting the value of the dependent variable based on the values of the independent variables.
- There are different types of regression (e.g., linear regression, logistic regression), each suited for specific types of relationships between variables.
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