Residual Analysis in Regression Model

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Residual analysis in regression is a critical process for assessing the goodness of fit of a regression model. Residuals are the differences between the observed values and the values predicted by the regression model. Analyzing these residuals helps to evaluate the assumptions and identify potential problems with the model. Here’s a comprehensive overview of residual analysis:

1. Residual Definition:

• Residual (eᵢ): The difference between the observed value (Yᵢ​) and the predicted value (Y^ᵢ​) for each data point in the dataset. eᵢ​=Yᵢ​−Y^ᵢ​

2. Assumptions in Regression:

• Linearity: The relationship between the variables should be linear.
• Independence: Residuals should be independent of each other.
• Homoscedasticity: Residuals should exhibit constant variance across all levels of the independent variable(s).
• Normality of Residuals: Residuals should follow a normal distribution.
• No Perfect Multicollinearity: Independent variables should not be perfectly correlated.

3. Steps in Residual Analysis:

a. Residual Plot:

• Visualize residuals by plotting them against the…