Linear Regression DATA-SCIENCE-FOUNDATIONS Practice Questions (Page 4)

Questions 16–20

1. 16foundation · easy

   Which of the following is a key assumption of linear regression?

   • AThe dependent variable must be categorical
   • BThe errors are normally distributed with a mean of zero
   • CThe independent variables must be normally distributed
   • DThere must be no relationship between the dependent and independent variables
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2. 17expert · hard

   A data scientist fits a linear regression model to predict energy consumption. The residual plot shows a clear funnel shape, and the Q-Q plot of residuals shows heavy tails. The data scientist is considering three transformations: (1) log-transform the dependent variable, (2) use weighted least squares, (3) add a quadratic term for the independent variable. Which action is most appropriate?

   • AUse weighted least squares to address heteroscedasticity, but this does not address non-normality.
   • BAdd a quadratic term to address non-linearity, but the funnel shape indicates heteroscedasticity, not non-linearity.
   • CLog-transform the dependent variable to address both heteroscedasticity and non-normality.
   • DRemove outliers to fix the heavy tails, but this does not address heteroscedasticity.
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4. 18application · medium

   A data scientist is modeling the relationship between the dosage of a drug and the patient's response. A scatter plot shows a clear curved pattern, with response increasing rapidly at low doses and leveling off at high doses. What should the data scientist do?

   • ARemove outliers from the data to make the relationship linear.
   • BTransform the dependent variable to make the relationship linear, but this is not always possible.
   • CFit a polynomial regression model, such as adding a squared term for dosage.
   • DUse a simple linear regression model because it is the standard approach.
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5. 19foundation · easy

   What is the purpose of cross-validation in linear regression model selection?

   • ATo assess how well the model generalizes to new data
   • BTo eliminate multicollinearity
   • CTo increase the R-squared of the model
   • DTo test the normality of residuals
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6. 20expert · hard

   A data science team is building a model to predict customer churn with 20 predictors. They have a dataset of 5,000 customers. They are considering two approaches: (1) stepwise regression using AIC, (2) cross-validation with a model that includes all predictors. Which approach is more likely to produce a model that generalizes well to new customers?

   • ACross-validation with all predictors, because it directly evaluates predictive performance on held-out data.
   • BBoth approaches are equally likely to generalize well.
   • CStepwise regression using AIC, because it selects a parsimonious model.
   • DNeither approach is appropriate; the team should use a more complex model like random forest.
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