Inferential Statistics PCAD-31 Practice Questions (Page 6)

Questions 26–30

1. 26foundation · easy

   Which scenario is best suited for linear regression?

   • APredicting a person's height in centimeters from their age
   • BPredicting whether a customer will churn (yes/no) from their usage data
   • CPredicting the number of website visits per day from advertising spend
   • DPredicting a customer's preferred product category (A, B, or C) from demographics
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2. 27expert · hard

   A researcher fits a linear regression model to predict employee salary from years of experience. The residual plot shows a clear funnel shape: the spread of residuals increases as years of experience increases. Which assumption of linear regression is most likely violated?

   • AIndependence of errors
   • BNormality of errors
   • CHomoscedasticity
   • DLinearity
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4. 28application · medium

   A data analyst generates 5,000 bootstrap samples from a dataset and computes the mean for each sample. The analyst wants a 90% confidence interval for the population mean. Which percentiles of the bootstrap means should be used?

   • AThe 10th and 90th percentiles
   • BThe 5th and 95th percentiles
   • CThe 1st and 99th percentiles
   • DThe 2.5th and 97.5th percentiles
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5. 29expert · hard

   A statistician uses bootstrapping to estimate the standard error of the sample median from a small dataset. The bootstrap distribution of the median is highly discrete, with only a few distinct values appearing. Which issue does this reveal?

   • AThe bootstrap samples are not being drawn with replacement
   • BThe bootstrap standard error will be underestimated
   • CThe bootstrap standard error should be computed using the normal approximation instead
   • DThe bootstrap distribution may not provide a smooth approximation to the true sampling distribution
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6. 30foundation · easy

   What is the role of the logit link function in logistic regression?

   • AIt ensures that the predicted probabilities are always exactly 0 or 1
   • BIt eliminates the need for maximum likelihood estimation
   • CIt transforms the probability of the outcome into a continuous value that can be modeled as a linear combination of predictors
   • DIt converts the outcome variable into a normally distributed variable
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