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

2. Residual (or error) Formula Observed Data - Predicted Data
(actual data from the chart – the value from the regression equation)

3. Determines the effectiveness of the regression model
Analyzing Residuals
Determines the effectiveness of the regression model

4. A scatterplot of Residuals vs. X
Residual Plots
A scatterplot of Residuals vs. X

5. Residual Plots Determine
If the line of best-fit (or regression equation) is appropriate, the plot will have a random scatter.
If another type of equation is necessary, the plot will have a pattern. Pattern = Problem

6. Example of Random Scatter

7. Examples
Determine, just by visual inspection, if the linear model is appropriate or inappropriate.

8. Linear model appropriate or inappropriate?

9. 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.

10. Linear model appropriate or inappropriate?

11. 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.

12. Linear model appropriate or inappropriate?

13. 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.

14. Linear model appropriate or inappropriate?

15. 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.

16. Example: Calculate Residual Tracking 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 37 73 54
Data from TI Activity for NUMB3RS Episode 202

17. Example: Calculate Residual Tracking 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
-1.9 28 47
47.5
-0.5 36 56
61.3
-5.3 17 27
28.5
-1.5 23 35
38.8
-3.8 41 65
70.0 -5 22
37.1
3.9 37 73
63.1
9.9 54
6.5
Data from TI Activity for NUMB3RS Episode 202

18. Good fit or not?

19. Classwork
Carnival Task

20. Homework
Worksheet