Modeling techniques such as linear and logistic regression MCQs

Linear Regression Basics:

What is the primary objective of linear regression?

A. To classify data into different categories
B. To predict continuous numeric values based on the relationship between variables
C. To identify outliers in a dataset
D. To visualize data patterns
Answer: B
In linear regression, what is the term used to represent the predicted value of the dependent variable?

A. Intercept
B. Slope
C. Residual
D. F-statistic
Answer: A
What does the coefficient of determination (R-squared) measure in linear regression?

A. The strength of the relationship between independent and dependent variables
B. The accuracy of model predictions
C. The variability explained by the regression model
D. The statistical significance of the model coefficients
Answer: C
Which assumption is essential for linear regression modeling?

A. Multicollinearity
B. Heteroscedasticity
C. Linearity
D. Overfitting
Answer: C
What happens if the residuals in linear regression violate the assumption of normality?

A. The model coefficients become biased.
B. The model predictions become less accurate.
C. The intercept term becomes undefined.
D. The model becomes overfitted.
Answer: A
Logistic Regression Fundamentals:
6. What type of data is logistic regression used to analyze?

A. Continuous numeric data

B. Categorical data with more than two categories

C. Binary categorical data

D. Ordinal data

Answer: C

In logistic regression, what does the logistic function (sigmoid function) do?

A. Maps the predicted values to a continuous range between 0 and 1
B. Computes the correlation between variables
C. Measures the interaction effects between variables
D. Normalizes the data distribution
Answer: A
What does the odds ratio represent in logistic regression?

A. The probability of an event occurring given the presence of certain conditions
B. The slope of the regression line
C. The ratio of explanatory variables in the model
D. The number of categories in the dependent variable
Answer: A
What is the purpose of the link function in logistic regression?

A. To calculate the intercept term
B. To connect the linear predictor to the probability of the dependent variable
C. To remove outliers from the dataset
D. To standardize the coefficients of the independent variables
Answer: B
How is the performance of a logistic regression model typically evaluated?

A. Mean Squared Error (MSE)
B. R-squared (R2)
C. Area Under the Receiver Operating Characteristic Curve (AUC-ROC)
D. F-statistic
Answer: C
Model Comparison and Application:
11. When should you use linear regression instead of logistic regression?
– A. When the dependent variable is categorical with more than two categories
– B. When the relationship between variables is non-linear
– C. When the dependent variable is binary or dichotomous
– D. When dealing with time series data
– Answer: B

In what scenarios would logistic regression be preferable over linear regression?

A. When the relationship between variables is assumed to be linear
B. When predicting probabilities of binary outcomes
C. When there are multicollinearity issues among independent variables
D. When the dataset contains outliers
Answer: B
How does regularization (e.g., Ridge or Lasso) help improve regression models?

A. By reducing the number of predictors and improving model interpretability
B. By increasing the complexity of the model to capture more data patterns
C. By normalizing the distribution of residuals
D. By removing outliers from the dataset
Answer: A
What is the primary drawback of using ordinary least squares (OLS) regression in the presence of multicollinearity?

A. It leads to biased estimates of coefficients.
B. It increases the variance of the model.
C. It assumes a linear relationship between variables.
D. It can inflate the standard errors of coefficients.
Answer: D
How does the AIC (Akaike Information Criterion) or BIC (Bayesian Information Criterion) aid in model selection?

A. By measuring the accuracy of model predictions
B. By penalizing model complexity to prevent overfitting
C. By visualizing data distributions
D. By evaluating the statistical significance of model coefficients
Answer: BWhat is the key assumption of linear regression regarding the relationship between the independent and dependent variables?

A. Non-linearity
B. Independence of errors
C. Multicollinearity
D. Heteroscedasticity
Answer: B
Which of the following methods is used to estimate the coefficients in linear regression?

A. Gradient Descent
B. K-nearest neighbors
C. Principal Component Analysis (PCA)
D. Decision Trees
Answer: A
What does the p-value associated with each coefficient in linear regression indicate?

A. The strength of the relationship between variables
B. The probability of observing a coefficient as extreme as the one computed, given that the null hypothesis is true
C. The accuracy of model predictions
D. The variance explained by the model
Answer: B
How does adding more predictors (independent variables) affect the adjusted R-squared value in linear regression?

A. It decreases the adjusted R-squared value.
B. It increases the adjusted R-squared value.
C. It has no effect on the adjusted R-squared value.
D. It increases the likelihood of multicollinearity.
Answer: A
When interpreting the intercept term in linear regression, what does a value of zero signify?

A. There is no relationship between the independent and dependent variables.
B. The dependent variable has a value of zero when all predictors are zero.
C. The model is overfitted.
D. The model is underfitted.
Answer: B
Logistic Regression Applications:
6. What transformation is applied to the linear predictor in logistic regression to obtain probabilities?

A. Exponential function

B. Logarithmic function

C. Sigmoid function

D. Square root function

Answer: C

In logistic regression, how are odds ratios calculated for each predictor variable?

A. By exponentiating the coefficient of each predictor
B. By dividing the coefficient of each predictor by the intercept
C. By standardizing the coefficients
D. By taking the reciprocal of the coefficient of each predictor
Answer: A
What is the purpose of the likelihood function in logistic regression?

A. To measure the goodness of fit of the model
B. To estimate the model coefficients
C. To normalize the distribution of residuals
D. To penalize complex models
Answer: B
When is logistic regression particularly useful in predictive modeling?

A. When predicting continuous numeric values
B. When dealing with time series data
C. When the dependent variable is binary or dichotomous
D. When analyzing multicollinear data
Answer: C
What does the Hosmer-Lemeshow test assess in logistic regression?

A. The linearity assumption of predictor variables
B. The normality of residuals
C. The goodness of fit of the logistic regression model
D. The interaction effects between predictor variables
Answer: C
Model Evaluation and Selection:
11. How does multicollinearity affect the interpretation of coefficients in linear regression?
– A. It inflates the standard errors of coefficients, making them less reliable.
– B. It increases the accuracy of model predictions.
– C. It removes outliers from the dataset.
– D. It improves the goodness of fit of the model.
– Answer: A

In logistic regression, what does the AUC-ROC curve measure?

A. The accuracy of the model predictions
B. The probability of the dependent variable being positive given a specific threshold
C. The linearity assumption of predictor variables
D. The trade-off between sensitivity and specificity
Answer: D
What is the primary advantage of using cross-validation in model evaluation?

A. It increases the bias of the model.
B. It evaluates the model’s performance on unseen data.
C. It reduces the complexity of the model.
D. It visualizes the distribution of residuals.
Answer: B
Which regularization technique is known for both shrinking coefficients and performing variable selection in linear regression?

A. Ridge regression
B. Lasso regression
C. Elastic Net
D. Principal Component Analysis (PCA)
Answer: B
How does the Bayesian Information Criterion (BIC) differ from the Akaike Information Criterion (AIC) in model selection?

A. BIC penalizes model complexity more heavily than AIC.
B. AIC is used for non-parametric models, while BIC is for parametric models.
C. BIC prefers more complex models with many predictors.
D. AIC is more suitable for small sample sizes compared to BIC.
Answer: A
Practical Applications and Interpretations:
16. When interpreting the odds ratio in logistic regression, what does a value greater than 1 indicate?
– A. The predictor has no effect on the probability of the outcome.
– B. The predictor increases the odds of the outcome occurring.
– C. The predictor decreases the odds of the outcome occurring.
– D. The predictor has a perfect prediction accuracy.
– Answer: B

What does the term “heteroscedasticity” refer to in the context of linear regression?

A. The non-linearity of the relationship between variables
B. The presence of outliers in the dataset
C. The unequal variance of errors across levels of the independent variables
D. The normal distribution of residuals
Answer: C
In logistic regression, how is the deviance statistic used to assess model fit?

A. It measures the overall variability explained by the model.
B. It compares the model with a saturated model.
C. It normalizes the distribution of residuals.
D. It estimates the model coefficients.
Answer: B
What role does the interaction term play in regression models?

A. It combines different variables to form new predictors.
B. It removes outliers from the dataset.
C. It penalizes large coefficients in the model.
D. It standardizes the coefficients of the predictors.
Answer: A
How does the F-statistic help in interpreting the overall significance of a linear regression model?

A. It measures the strength of the relationship between independent and dependent variables.
B. It evaluates the goodness of fit of the model.
C. It tests the joint significance of all predictors in the model.
D. It normalizes the distribution of residuals.
Answer: C

Modeling techniques such as linear and logistic regression MCQs

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