Foundations of Linear Regression: The 4 Key Assumptions

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Linear regression relies on several assumptions to provide valid and reliable results. Here are the four key assumptions underlying a linear regression model:

1. Linearity:

• Assumption: The relationship between the independent variable(s) and the dependent variable is linear.
• Rationale: The model assumes that changes in the dependent variable are linearly related to changes in the independent variable(s).
• Assessment:You can assess this assumption by visually inspecting scatter plots and residual plots.

2. Independence of Residuals:

• Assumption: The residuals (the differences between observed and predicted values) are independent of each other.
• Rationale: Independence of residuals is crucial for valid statistical inference. If residuals are correlated, it may suggest that there is still information in the data that the model has not captured. Time series data, in particular, may violate this assumption.

3. Homoscedasticity (Constant Variance of Residuals):

• Assumption: The variance of the residuals is constant across all levels of the independent variable(s).