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Residuals quiz

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  • What is a residual in linear regression?
    A residual is the vertical distance from a data point to the regression line, calculated as y - ŷ.
  • How do you calculate a residual for a data point?
    Subtract the predicted value (ŷ) from the observed value (y) for that data point.
  • What does the least squares method do in linear regression?
    It finds the line of best fit by minimizing the sum of the squared residuals.
  • What is the formula for a residual?
    The formula is d = y - ŷ, where y is the observed value and ŷ is the predicted value.
  • Can residuals be negative or positive?
    Yes, residuals can be either negative or positive depending on whether the observed value is below or above the predicted value.
  • What is a residual plot?
    A residual plot is a graph that shows residuals on the y-axis and the original x values on the x-axis.
  • What does a random pattern in a residual plot indicate?
    A random pattern suggests that the regression model is a good fit for the data.
  • What does a discernible pattern in a residual plot suggest?
    A discernible pattern indicates that the regression model may not be a good fit and another model may be needed.
  • What is the purpose of plotting residuals?
    Plotting residuals helps assess whether the regression line is a good fit for the data.
  • What does it mean if residuals oscillate in a plot?
    Oscillating residuals suggest that a linear model may not be appropriate and another type of model may be needed.
  • What does it mean if residuals diverge in a plot?
    Diverging residuals indicate that the standard deviation is not constant and the linear model may not fit well.
  • How do you find the predicted value (ŷ) for a given x?
    Plug the x value into the regression equation to calculate ŷ.
  • What axis are residuals plotted on in a residual plot?
    Residuals are plotted on the y-axis in a residual plot.
  • What should you do if the residual plot shows a pattern?
    If a pattern is present, consider using a different model to better fit the data.
  • Why is it important to check residuals after fitting a regression line?
    Checking residuals helps verify if the linear regression model is appropriate for the data.