FAST Regression Analysis 2

Question 1

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

Accepted Answer

The slope (rate of change)

Answer

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

Question 2

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

Accepted Answer

The error term must have zero mean

Answer

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

Question 3

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?

Accepted Answer

The new predictor does not add meaningful explanatory power

Answer

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

Question 4

Heteroscedasticity in regression refers to:

Accepted Answer

Non-constant variance of the residuals across values of x

Answer

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

Question 5

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

Accepted Answer

No multicollinearity with other predictors

Answer

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

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