1. Residuals Learning Target:
Students can informally assess the fit of a function by plotting and analyzing residuals.
From the Carnegie Foundation math.mtsac.edu/statway/lesson_3.3.1_version1.5A

2. Residual is another word for ERROR
Residuals
Residual is another word for ERROR

3. Residuals
To find the residual you take the ACTUAL data and SUBTRACT the PREDICTED data.

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

5. Residual Plots
A residual plot is another type of SCATTERPLOT that shows the relationship of the residual to the x value.

6. Residual Plots Determine
If the regression model is appropriate, then the residual plot will have a RANDOM scatter.
If the residual plot creates a pattern then the regression model is NOT A GOOD FIT. Pattern = Problem

7. Example of Random Scatter

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

9. Linear model appropriate or inappropriate?

10. 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.

11. Linear model appropriate or inappropriate?

12. 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.

13. Linear model appropriate or inappropriate?

14. 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.

15. Linear model appropriate or inappropriate?

16. 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.

17. Example: Calculate Residual
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

18. Example: Calculate Residual
Total Time (minutes)
Total Distance (miles)
Predicted Total Distance
Residuals
(observed – predicted) 32 51
54.4
-3.4 19 30
31.9 28 47
47.5 36 56
61.3 17 27
28.5 23 35
38.8 41 65
70.0 22
37.1 37 73
63.1 54
Data from TI Activity for NUMB3RS Episode 202

19. Example: Calculate Residual
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

20. Good fit or not?
Residual
Total Time

21. Good fit or not?
Residual
Total Time