Table of Contents
Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It helps in understanding how the typical value of the dependent variable changes when any one of the independent variables is varied, while the others are held fixed.
Calculations in Regression Analysis
The core calculation in regression involves estimating the coefficients that minimize the difference between observed and predicted values. The most common method is least squares, which minimizes the sum of squared residuals.
Key calculations include:
- Calculating the mean of variables
- Computing covariance and variance
- Estimating regression coefficients using formulas such as β = (X’X)^-1 X’Y
- Assessing the goodness of fit with R-squared
Model Selection Techniques
Selecting the appropriate regression model involves evaluating various criteria to balance model complexity and accuracy. Common techniques include:
- Adjusted R-squared
- Akaike Information Criterion (AIC)
- Bayesian Information Criterion (BIC)
- Cross-validation methods
These techniques help in choosing models that generalize well to new data and avoid overfitting.
Practical Considerations
When performing regression analysis, it is important to check assumptions such as linearity, independence, homoscedasticity, and normality of residuals. Violations can lead to inaccurate models.
Data preprocessing, including handling missing values and feature scaling, can improve model performance and calculation stability.