Linear Regression DATA-SCIENCE-FOUNDATIONS Practice Questions (Page 6)

Questions 26–30

1. 26foundation · easy

   What pattern in a residual plot (residuals vs. fitted values) suggests a violation of the linearity assumption?

   • AA random scatter of points around zero
   • BA clear curved pattern (e.g., U-shape or inverted U)
   • CPoints that are all above zero
   • DA funnel shape where the spread increases with fitted values
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2. 27application · medium

   After fitting a linear regression model, an analyst examines a residual plot of residuals versus fitted values. The plot shows a clear funnel shape: residuals are small for low fitted values and spread out widely for high fitted values. Which model assumption is most likely violated?

   • AIndependence of errors
   • BHomoscedasticity
   • CNormality of errors
   • DLinearity
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4. 28application · medium

   A data scientist is building a model to predict house prices using both 'number of bedrooms' and 'total rooms' as predictors. The model output shows that neither coefficient is statistically significant, but the overall F-test is significant. What is the most likely explanation?

   • AThe predictors are not linearly related to the outcome
   • BThe sample size is too small
   • CThe model is overfitted
   • DMulticollinearity between the two predictors
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5. 29foundation · easy

   In which scenario is linear regression inappropriate?

   • AWhen the independent variables are continuous
   • BWhen the dependent variable is binary (e.g., yes/no)
   • CWhen the relationship between variables is linear
   • DWhen the sample size is large
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6. 30foundation · easy

   If a 95% confidence interval for a regression coefficient is [0.2, 0.8], what can be concluded?

   • AThere is a 95% probability that the true coefficient lies between 0.2 and 0.8
   • BThe coefficient is exactly 0.5
   • CThe coefficient is definitely not zero
   • DWe are 95% confident that the true coefficient lies between 0.2 and 0.8
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