Practical Data Science using Python - Linear Regression OLS Assumptions and Testing

The video tutorial covers the concept of error terms in linear regression, emphasizing that the population mean of error terms should be zero. It discusses key assumptions such as uncorrelated predictor variables, constant variance (homoscedasticity), and absence of multicollinearity. The tutorial also explains the importance of R-squared and adjusted R-squared values, coefficients, and p-values in model evaluation. Techniques like variance inflation factor (VIF) and recursive feature elimination (RFE) are introduced for optimizing models. Finally, it highlights the significance of residual analysis and probability plots in validating model assumptions.

What is the population mean of error terms in a linear regression model?

• 0

• 1

• 0.5

• -1

Which assumption states that predictor variables should not be correlated with the error term?

• Homoscedasticity

• Multicollinearity

• No correlation with error term

• Independence

What does the absence of multicollinearity ensure in a linear regression model?

• Predictor variables are correlated with the target variable

• Predictor variables are independent of each other

• Error terms have constant variance

• Error terms are normally distributed

Why is the adjusted R-squared value preferred over the R-squared value?

• It does not change with more features

• It is easier to calculate

• It penalizes the addition of irrelevant features

• It is always higher

What does a P-value greater than 0.05 indicate about a predictor feature?

• The feature has a strong correlation

• The feature is significant

• The feature is not significant

• The feature should be included

What is the purpose of the Variance Inflation Factor (VIF) in model optimization?

• To measure the correlation between predictors

• To determine the model's accuracy

• To evaluate the model's complexity

• To assess the normality of residuals

What does Recursive Feature Elimination (RFE) help with in linear regression?

• Selecting important features

• Improving residual normality

• Increasing model complexity

• Reducing model accuracy

What does a probability plot assess in residual analysis?

• The normality of residuals

• The linearity of the model

• The correlation between predictors

• The variance of error terms

What does homoscedasticity imply about the variance of residuals?

• Variance decreases with predicted values

• Variance increases with predicted values

• Variance is zero

• Variance remains constant across predicted values

What is the significance of a straight line in a probability plot of residuals?

• Residuals are correlated

• Residuals are normally distributed

• Residuals have constant variance

• Residuals are not normally distributed