Skip to main content
Pearson+ LogoPearson+ Logo
Back

Residuals quiz #1

Control buttons has been changed to "navigation" mode.
1/17
  • What is a residual in linear regression, and what does it mean when a residual is positive?
    A residual is the vertical distance between an observed data point and the predicted value from the regression line, calculated as residual = y - ŷ. A positive residual means the observed value is above the predicted value.
  • What does a residual value of -0.8 indicate in reference to the line of best fit?
    A residual value of -0.8 means the observed value is 0.8 units below the value predicted by the line of best fit.
  • How can you determine from a residual plot if the line of best fit is appropriate for the data?
    If the residual plot shows a random scatter of points with no discernible pattern, the line of best fit is appropriate. Patterns or systematic structures suggest the model may not be suitable.
  • What characteristics of a residual plot indicate a good least squares regression line (LSRL) model?
    A good LSRL model is indicated by a residual plot where the residuals are randomly scattered around zero, with no clear pattern or systematic structure.
  • What is a residual in regression analysis, and when is a residual considered positive?
    A residual is the difference between the observed value and the predicted value from the regression line (y - ŷ). It is positive when the observed value is greater than the predicted value.
  • What is a residual in linear regression, and what does a positive residual indicate?
    A residual is the difference between the observed value and the predicted value (y - ŷ). A positive residual indicates the observed value is above the predicted value.
  • What does a residual value of 1.3 mean in reference to the line of best fit for a data set?
    A residual value of 1.3 means the observed value is 1.3 units above the value predicted by the line of best fit.
  • How does the pattern of points in a residual plot help assess the fit of a regression line?
    A random pattern of points in a residual plot suggests a good fit for the regression line, while a discernible pattern indicates the model may not be appropriate.
  • What does a plot of residuals versus fitted values reveal about the appropriateness of a regression model?
    A plot of residuals versus fitted values reveals whether the residuals are randomly distributed. Random scatter indicates an appropriate model; patterns suggest the model may not fit well.
  • How is a point represented on a residual plot for a given data pair (x, y)?
    On a residual plot, each point is plotted at its original x-value and its residual value (y - ŷ) on the y-axis.
  • What does the independent observation assumption mean for the residuals plot in regression analysis?
    The independent observation assumption means that the residuals should not show patterns related to the order of data collection; each residual should be independent of the others.
  • What should a residual plot look like if the regression line fits the data well?
    If the regression line fits the data well, the residual plot should show residuals randomly scattered around zero with no systematic pattern.
  • What is a residual in regression, and what does it mean when a residual is positive?
    A residual is the difference between the observed value and the predicted value (y - ŷ). A positive residual means the observed value is greater than the predicted value.
  • What is a residual in regression analysis, and what does it mean when a residual is positive?
    A residual is the vertical distance between an observed value and the predicted value from the regression line. A positive residual means the observed value is above the predicted value.
  • What does it mean when a residual is positive in linear regression?
    A positive residual means that the observed value is greater than the predicted value from the regression line, indicating the data point lies above the line of best fit.
  • What does a negative residual indicate in the context of regression analysis?
    A negative residual indicates that the observed value is less than the predicted value from the regression line, meaning the data point lies below the line of best fit.
  • How are residuals calculated in linear regression, and what do their signs represent?
    Residuals are calculated as the observed value minus the predicted value (residual = y - ŷ). A positive residual means the point is above the regression line, while a negative residual means it is below the line.