Question

In: Statistics and Probability

What can a plot of the residuals alert us about?

What can a plot of the residuals alert us about?

Solutions

Expert Solution

Solution :-

A residual value is a measure of how much a regression line vertically misses a data point. Regression lines are the best fit of a set of data. If we  think of the lines as averages; a few data points will fit the line and others will miss.

A residual plot has the Residual Values on the vertical axis; the horizontal axis displays the independent variable.

Residual plot is typically used to find problems with regression. Some data sets are not good candidates for regression, including:

  • Heteroscedastic data (points at widely varying distances from the line).
  • Data that is non-linearly associated.
  • Data sets with outliers.

These problems are more easily seen with a residual plot than by looking at a plot of the original data set. Ideally, residual values should be equally and randomly spaced around the horizontal axis.

In one word, the analysis of residuals is a powerful diagnostic tool, as it will help to assess, whether some of the underlying assumptions of regression have been violated.


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