FAST Regression Analysis 3

Question 1

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

Accepted Answer

Minimize the sum of squared residuals

Answer

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

Question 2

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

Accepted Answer

Has an unusual value on the predictor(s)

Answer

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

Question 3

Cook's Distance is used in regression to measure:

Accepted Answer

The overall influence of an observation on all fitted values

Answer

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

Question 4

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

Accepted Answer

The approximate percentage change in Y per unit increase in X

Answer

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

Question 5

The Durbin-Watson statistic is primarily used to detect:

Accepted Answer

Autocorrelation in the residuals

Answer

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

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