Explanation:

• R-squared and adjusted R-squared are both statistics that measure the goodness of fit for a regression model. However, they serve slightly different purposes:
  • R-squared measures the proportion of the variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, where 1 means a perfect fit.
  • Adjusted R-squared adjusts the R-squared value based on the number of predictors in the model. It accounts for the possibility of overfitting, which can occur when too many variables are included in the model.

Key Talking Points:

• R-squared:
  • Measures the proportion of variance explained by the model.
  • Does not decrease with the addition of new predictors.
• Adjusted R-squared:
  • Adjusts for the number of predictors in the model.
  • Can decrease if the added predictors do not improve the model significantly.

NOTES:

Reference Table:

Follow-Up Questions and Answers:

• Why is adjusted R-squared important?

  • Adjusted R-squared is crucial when comparing models with different numbers of predictors because it penalizes the inclusion of variables that do not improve the model significantly, helping to prevent overfitting.

• Can adjusted R-squared be lower than R-squared?

  • Yes, adjusted R-squared can be lower than R-squared if the additional predictors do not contribute to explaining the variance in the dependent variable.

Pseudocode (R):

   # Simple linear regression in R
   model <- lm(y ~ x1 + x2 + x3, data = dataset)

   # Extract R-squared and adjusted R-squared
   r_squared <- summary(model)$r.squared
   adj_r_squared <- summary(model)$adj.r.squared

   print(paste("R-squared:", r_squared))
   print(paste("Adjusted R-squared:", adj_r_squared))

This comprehensive explanation, along with the table and code snippet, provides a well-rounded understanding of the differences between R-squared and adjusted R-squared, making it suitable for a technical interview at a FAANG company.

CHAPTER: Time Series Analysis