FAST Regression Analysis 2 — Questions and Answers
Question 1: In a regression equation ŷ = 5 + 3x, what does the value 3 represent?
- The y-intercept
- The slope (rate of change) (Correct answer)
- The correlation coefficient
- The residual
Correct 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.
Question 2: Which condition must be met for ordinary least squares (OLS) regression to produce unbiased estimates?
- Errors must be normally distributed
- The error term must have zero mean (Correct answer)
- All variables must be standardized
- Sample size must exceed 100
Correct 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).
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?
- The new predictor significantly improves the model
- The new predictor does not add meaningful explanatory power (Correct answer)
- Multicollinearity has been eliminated
- The sample size is too small
Correct 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.
Question 4: Heteroscedasticity in regression refers to:
- Predictors that are highly correlated with each other
- Non-constant variance of the residuals across values of x (Correct answer)
- Residuals that follow a non-normal distribution
- A non-linear relationship between x and y
Correct 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.
Question 5: If the Variance Inflation Factor (VIF) for a predictor equals 1, this indicates:
- Severe multicollinearity
- Moderate multicollinearity
- No multicollinearity with other predictors (Correct answer)
- Perfect correlation with the outcome
Correct answer: No multicollinearity with other predictors
A VIF of 1 means the predictor is completely uncorrelated with all other predictors in the model.
Question 6: A residual plot shows a curved (U-shaped) pattern against fitted values. The best remedy is to:
- Remove outliers from the dataset
- Add a polynomial term or transform a variable (Correct answer)
- Increase the sample size
- Switch to logistic regression
Correct 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.
Question 7: In multiple regression, the partial regression coefficient for predictor X₁ estimates the effect of X₁ on Y:
- Ignoring all other predictors
- Holding all other predictors constant (Correct answer)
- After removing X₁ from the model
- Only when X₁ is the strongest predictor
Correct answer: Holding all other predictors constant
Partial coefficients isolate the unique contribution of each predictor while statistically controlling for the others.
FAST Regression Analysis 2
In a regression equation ŷ = 5 + 3x, what does the value 3 represent?