Regression Analysis Flashcards

In a regression equation ŷ = 5 + 3x, what does the value 3 represent?

Answer: The slope (rate of change)

The coefficient of x (3) is the slope, indicating ŷ increases by 3 units for each 1-unit increase in x.

Which condition must be met for ordinary least squares (OLS) regression to produce unbiased estimates?

Answer: The error term must have zero mean

A key Gauss-Markov assumption is that the expected value of the error term equals zero (E[ε] = 0).

A researcher finds that adding a third predictor raises R² from 0.72 to 0.73 but drops adjusted R² from 0.71 to 0.70. What should she conclude?

Answer: The new predictor does not add meaningful explanatory power

Adjusted R² penalizes for unnecessary predictors; a decline despite rising R² means the added variable is not worth its cost in degrees of freedom.

Heteroscedasticity in regression refers to:

Answer: Non-constant variance of the residuals across values of x

Heteroscedasticity means the spread (variance) of residuals changes systematically across levels of the predictor.

If the Variance Inflation Factor (VIF) for a predictor equals 1, this indicates:

Answer: No multicollinearity with other predictors

A VIF of 1 means the predictor is completely uncorrelated with all other predictors in the model.

A residual plot shows a curved (U-shaped) pattern against fitted values. The best remedy is to:

Answer: Add a polynomial term or transform a variable

A curved residual pattern signals non-linearity; adding a squared term or applying a log/square-root transformation corrects this.

In multiple regression, the partial regression coefficient for predictor X₁ estimates the effect of X₁ on Y:

Answer: Holding all other predictors constant

Partial coefficients isolate the unique contribution of each predictor while statistically controlling for the others.