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RESIDUALS
Residuals (Error)
The difference between the observed y and the predicted y
Observed Y – Predicted Y
Determines the effectiveness of the regression model
Given to you in the chart Get by plugging into the equation
Residual Plots Determine
If the model is appropriate, then the plot will have a random scatter.
If another model is necessary, the plot will have a noticeable pattern.
Pattern = Problem!
Linear model appropriate or inappropriate?
The only way to know is to see the residual plot.
1. Does there appear to be a pattern in the residual plot?Yes, this shape is
called a quadratic.2. Does this
support your original guess?You must now
see that a linear model does NOT fit this data. Not scattered!
Linear model appropriate or inappropriate?
The only way to know is to see the residual plot.
1. Does their appear to be a pattern in the residual plot?Yes, it fans out
as x increases.2. Does this support your original guess?
You must now see that a linear model does NOT fit this data. Fan Pattern.
Linear model appropriate or inappropriate?
The only way to know is to see the residual plot.
1. Does their appear to be a pattern in the residual plot?Yes, it looks quadratic.
2. Does this support your original guess?
This was very tricky. The scale was very small. You must now see that a linear model does NOT fit this data.
Linear model appropriate or inappropriate?
The only way to know is to see the residual plot.
1. Does their appear to be a pattern in the residual plot?Yes, it seems to decrease as x increases.2. Does this support your original guess?This was tricky.
You must now see that a linear model does NOT fit this data.
Example 1: Calculate Residualfrom this data set:
X Y PredictedResiduals(observed – predicted)
1 4
2 12
3 18
4 23
5 24
6 28
4.6 2.07y x
=
===
=6.67 -2.67
Example 1: Calculate Residualfrom this data set:
X Y PredictedResiduals(observed – predicted)
1 4 6.67 -2.67
2 12 11.27
3 18 15.87
4 23 20.47
5 24 25.07
6 28 29.67
4.6 2.07y x
=
===
=
Good fit or not? Is there a Pattern?
0 1 2 3 4 5 6 7
-3
-2
-1
0
1
2
3
There is no pattern. This makes this line a good fit.
Example 2: Calculate ResidualTracking Cell Phone Use over 10 days
Total Time (minutes)
Total Distance
(miles
Predicted Total
Distance
Residuals(observed – predicted)
32 51 54.4 -3.4
19 30 31.9
28 47
36 56
17 27
23 35
41 65
22 41
37 73
28 54
1.73 0.96y x
=========
=
Example: Calculate ResidualTracking Cell Phone Use over 10 days
Total Time (minutes)
Total Distance (miles)
Predicted Total Distance
Residuals(observed – predicted)
32 51 54.4 -3.4
19 30 31.9 -1.928 47 47.5 -0.536 56 61.3 -5.317 27 28.5 -1.523 35 38.8 -3.841 65 70.0 -522 41 37.1 3.937 73 63.1 9.928 54 47.5 6.5
1.73 0.96y x
Good fit or not? Is there a Pattern?
15 20 25 30 35 40 45
-8
-6
-4
-2
0
2
4
6
8
10
12
The plots begin to fan out in a “U” shape, so it is not a great fitting line.
YES, I THINK THIS STUFF IS HARD TOO!
HOMEWORK :RESIDUALSWORKSHEET
We will go over this tomorrow in detail, I promise
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