Which of the following is desirable with reference to linear regression models?

Correct option is A

Introduction

• Linear regression is a fundamental statistical technique used for modeling relationships between dependent and independent variables.
• For a regression model to be valid, reliable, and produce unbiased estimates, it must satisfy certain assumptions and properties.

Information Booster:

• Homoscedasticity 
• Constant variance of residuals (errors) across all levels of independent variables.
• Ensures equal reliability of predictions across the range of data
  
• Allows valid hypothesis testing (t-tests, F-tests)
  
• Produces Best Linear Unbiased Estimators (BLUE) via OLS
  
• Standard errors are correctly estimated
  
• Confidence intervals remain valid
  
• Mathematical Expression: Var(εᵢ) = σ² (constant for all observations)
• Violation (Heteroscedasticity):
• Cone-shaped residual patterns
  
• Leads to inefficient estimates and invalid standard errors
  
• Remedies: weighted least squares, transformation, robust standard errors

Additional knowledge:

• Multicollinearity
• High correlation among independent variable
• Inflates standard errors of coefficients
• VIF (Variance Inflation Factor) > 10 indicates problem
• Autocorrelation among Residuals
• Residuals are correlated with each other (common in time series)
• Violates independence assumption
• Correlation between Residuals and Independent Variables
• Indicates endogeneity problem
• Violates exogeneity assumption: E(ε|X) = 0