Regression Analysis is a statistical method used to examine the relationship between a dependent variable and one or more independent variables. It helps in understanding how the value of the dependent variable changes when any one of the independent variables is varied, while others are held constant. The most commonly used form is linear regression, where the relationship is modeled through a straight line (Y = a + bX).
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Purpose of Regression
The main objective of regression analysis is prediction and forecasting, as well as measuring the strength of relationships among variables. It is widely used in economics, finance, marketing, management, engineering, and scientific research.
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Advantages of Regression Analysis
1. Prediction and Forecasting: It enables future projections based on past data trends.
2. Quantitative Decision Making: Businesses use regression for informed decision-making.
3. Measurement of Relationships: It quantifies how strongly variables are related.
4. Helps in Hypothesis Testing: Used to test economic theories and scientific models.
5. Control of Confounding Variables: Helps isolate the effect of individual variables.
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Limitations of Regression Analysis
1. Assumption Dependent: It assumes linearity, constant variance, and normality, which may not hold in real-world data.
2. Causation vs Correlation: Regression shows association, not causation.
3. Affected by Outliers: Extreme values can distort results significantly.
4. Multicollinearity: When independent variables are highly correlated, it becomes difficult to interpret the effect of each.
5. Overfitting Risk: Adding too many variables may make the model too complex and reduce predictive accuracy.
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Regression Coefficients (in Brief)
In the regression equation Y = a + bX:
a is the intercept: the expected value of Y when X = 0.
b is the slope coefficient: it shows the amount by which Y changes for a one-unit change in X.
In multiple regression, there are multiple slope coefficients (b₁, b₂, b₃, …), each representing the effect of one independent variable on the dependent variable, holding others constant.
