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Error = observed - predicted
- perfect line will have the least error Residual - the difference between an observed value and the value predicted by the regression line. residual = observed y - predicted y
3.2 Residuals
Also known as Residual plot - plots the residuals on the vertical axis against the explanatory variable on the horizontal axis A residual plot helps us determine how well a regression line fits the data. Important property of residuals their sum = zero
*^ *
Scatter Plot 0 Residual Plot
Analyzing residual plots: ÿ A curved pattern shows the overall pattern is not linear therefore the regression line is not a good model. ÿ (^) A megaphone pattern will be less accurate for larger values of x. ÿ (^) Ideal residuals are scattered.
Interpretation of the residual. The regression line overpredicts/underpredicts the name of y by residual units of y.
Ex.
The following data consists of students scores on the chapter
and 2 tests.
Test #1: 88, 82, 78, 96, 78, 84, 91, 83, 85, 68, 92, 72
Test #2: 100, 86, 67, 91, 71, 102, 91, 81, 86, 91, 89, 78
a) Make a scatter plot of the data
b) Find the LSRL, plot it on your scatter plot.
c) Find the residual for student #1. Show your work.
d) Make a residual plot of the data.
