Review Homework

Residuals

From the Carnegie Foundation math.mtsac.edu/statway/lesson_3.3.1_version1.5A

Residual (or error) Observed y MINUS predicted y

Analyzing ResidualsDetermines the effectiveness of the regression model

Residual PlotsA scatterplot of Residuals vs. X

Residual Plots Determine

If it the model is appropriate, then the plot will have a random scatter.

If another model is necessary, the plot will have a pattern. Pattern = Problem

Example of Random Scatter

ExamplesDetermine, just by visual inspection, if

the linear model is appropriate or inappropriate.

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, quadratic.2. Does this support your original guess?

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 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.

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 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: Calculate ResidualTracking Cell Phone Use over 10 days

Total Time (minutes)

Total Distance (miles

Predicted Total Distance

Residuals(observed – predicted)

32 51 54.4 -3.419 30 31.928 4736 5617 2723 3541 6522 4137 7328 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 -3.419 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?

15 20 25 30 35 40 45

-8

-6

-4

-2

0

2

4

6

8

10

12

HomeworkFinish Study Guide