AIC (Akaike Information Criterion)
What is the main purpose of AIC in model selection?
a) To maximize the number of predictors in a model
b) To identify the model with the lowest error rate
c) To balance model fit and complexity
d) To minimize the residual sum of squares
Show Answer
Answer: c) To balance model fit and complexity
Explanation: AIC aims to find the model that best balances goodness-of-fit and model complexity to avoid overfitting.
How does the AIC penalize models?
a) By adding a penalty proportional to the number of parameters in the model
b) By subtracting a penalty based on the model accuracy
c) By multiplying the likelihood by the number of parameters
d) By dividing the residual sum of squares by the number of observations
Show Answer
Answer: a) By adding a penalty proportional to the number of parameters in the model
Explanation: AIC includes a penalty term that increases with the number of parameters to discourage overfitting.
Which of the following models is preferred based on AIC values?
a) The model with the highest AIC value
b) The model with the lowest AIC value
c) The model with the AIC value closest to zero
d) The model with the AIC value equal to the number of observations
Show Answer
Answer: b) The model with the lowest AIC value
Explanation: A lower AIC value indicates a better balance between fit and complexity.
BIC (Bayesian Information Criterion)
What is the main difference between AIC and BIC?
a) BIC does not penalize model complexity
b) BIC includes a stronger penalty for the number of parameters compared to AIC
c) AIC is used for time series data, while BIC is used for cross-sectional data
d) AIC and BIC are equivalent and there is no difference
Show Answer
Answer: b) BIC includes a stronger penalty for the number of parameters compared to AIC
Explanation: BIC imposes a larger penalty on the number of parameters, which is more pronounced with larger sample sizes.
In the context of BIC, what is the effect of increasing the sample size?
a) The penalty for additional parameters decreases
b) The penalty for additional parameters increases
c) The BIC value becomes irrelevant
d) The BIC value becomes negative
Show Answer
Answer: b) The penalty for additional parameters increases
Explanation: The BIC penalty term grows with the logarithm of the sample size, making it more stringent as the sample size increases.
Which of the following models is preferred based on BIC values?
a) The model with the highest BIC value
b) The model with the lowest BIC value
c) The model with the BIC value closest to zero
d) The model with the BIC value equal to the number of parameters
Show Answer
Answer: b) The model with the lowest BIC value
Explanation: A lower BIC value indicates a better model according to the BIC criterion.
Adjusted R-squared
What is the purpose of Adjusted R-squared in regression analysis?
a) To increase the R-squared value by adding more predictors
b) To provide a measure of goodness-of-fit adjusted for the number of predictors
c) To simplify the model by removing insignificant predictors
d) To maximize the correlation between predictors and the target variable
Show Answer
Answer: b) To provide a measure of goodness-of-fit adjusted for the number of predictors
Explanation: Adjusted R-squared adjusts the R-squared value to account for the number of predictors in the model.
How does Adjusted R-squared differ from R-squared?
a) Adjusted R-squared decreases when irrelevant predictors are added
b) Adjusted R-squared always equals R-squared
c) Adjusted R-squared ignores the number of predictors
d) Adjusted R-squared increases regardless of the relevance of predictors
Show Answer
– Answer: a) Adjusted R-squared decreases when irrelevant predictors are added
– Explanation: Unlike R-squared, Adjusted R-squared can decrease if the added predictors do not improve the model fit.
Which of the following statements is true regarding Adjusted R-squared?
a) It always decreases when more predictors are added
b) It always increases when more predictors are added
c) It can increase or decrease depending on the significance of the added predictors
d) It remains constant regardless of the number of predictors
Show Answer
Answer: c) It can increase or decrease depending on the significance of the added predictors
Explanation: Adjusted R-squared takes into account the number of predictors and can go up or down based on their contribution to the model.
Mixed Questions
If two models have the same number of predictors but different AIC values, which model is preferred?
a) The model with the higher AIC value
b) The model with the lower AIC value
c) The model with the AIC value closest to zero
d) Both models are equally preferred
Show Answer
Answer: b) The model with the lower AIC value
– Explanation: A lower AIC value indicates a better model by balancing fit and complexity.
Which of the following statements is true regarding AIC, BIC, and Adjusted R-squared?
a) AIC and BIC always lead to the same model selection
b) Adjusted R-squared always leads to more complex models than AIC and BIC
c) AIC, BIC, and Adjusted R-squared may lead to different model selections depending on the data
d) Adjusted R-squared does not consider the number of predictors in the model
Show Answer
Answer: c) AIC, BIC, and Adjusted R-squared may lead to different model selections depending on the data
– Explanation: These criteria may lead to different model selections because they balance fit and complexity differently.
Which criterion explicitly incorporates the sample size in its calculation?
a) R-squared
b) BIC
c) Adjusted R-squared
d) None of the above
Show Answer
Answer: b) BIC
– Explanation: BIC includes the sample size in its penalty term, which affects the selection of models more significantly as the sample size increases.
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