Regression Analysis Flashcards

Which of the following is the primary goal of the least squares method in regression?

Answer: Minimize the sum of squared residuals

OLS finds the line (or hyperplane) that minimizes the sum of squared differences between observed and predicted values.

A leverage point in regression is best described as an observation that:

Answer: Has an unusual value on the predictor(s)

High-leverage points have extreme x values and can exert strong influence on the estimated regression line.

Cook's Distance is used in regression to measure:

Answer: The overall influence of an observation on all fitted values

Cook's D combines each observation's leverage and residual to quantify how much it shifts the entire set of fitted values if removed.

When using a log transformation on the dependent variable (ln Y), the regression coefficient b₁ is best interpreted as:

Answer: The approximate percentage change in Y per unit increase in X

In a log-linear model, multiplying b₁ by 100 gives the approximate percentage change in Y for a one-unit increase in X.

The Durbin-Watson statistic is primarily used to detect:

Answer: Autocorrelation in the residuals

The Durbin-Watson test checks whether consecutive residuals are correlated, a common violation in time-series data.

In simple linear regression, if r = –0.85, which statement is correct?

Answer: As X increases, Y tends to decrease strongly

r = –0.85 indicates a strong negative linear relationship: higher X values are associated with lower Y values.

Ridge regression differs from ordinary least squares by:

Answer: Adding a penalty term (λ) that shrinks coefficients toward zero

Ridge regression adds an L2 penalty (λ∑β²) to the OLS cost function, stabilizing estimates when multicollinearity is present.