Contents
What do residuals tell us about a data point?
Residuals help to determine if a curve (shape) is appropriate for the data. A residual is the difference between what is plotted in your scatter plot at a specific point, and what the regression equation predicts “should be plotted” at this specific point.
What does it mean when residuals have a pattern?
The residual plot shows a fairly random pattern – the first residual is positive, the next two are negative, the fourth is positive, and the last residual is negative. This random pattern indicates that a linear model provides a decent fit to the data.
Do residuals form a pattern?
Student: Hey, the residuals form a pattern! They are definitely not randomly scattered, but instead they are making a curve. This line was not a good fit. Therefore, in the case of the line of best fit often the positive error will balance out the negative error so that the sum of the residuals will be approximately 0.
Where are the data points on the residuals versus fits plot?
Now look at how and where these five data points appear in the residuals versus fits plot. Their fitted value is about 14 and their deviation from the residual = 0 line shares the same pattern as their deviation from the estimated regression line. Do you see the connection?
Which is the residual of the estimated regression line?
Any data point that falls directly on the estimated regression line has a residual of 0. Therefore, the residual = 0 line corresponds to the estimated regression line. This plot is a classical example of a well-behaved residuals vs. fits plot.
What is the fitted value of a residual?
Their fitted value is about 14 and their deviation from the residual = 0 line shares the same pattern as their deviation from the estimated regression line. Do you see the connection? Any data point that falls directly on the estimated regression line has a residual of 0.
Where are the residuals on a scatter plot?
Note that, as defined, the residuals appear on the y axis and the fitted values appear on the x axis. You should be able to look back at the scatter plot of the data and see how the data points there correspond to the data points in the residual versus fits plot here.