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Warm-Up Math Social
Studies P.E.
Women 16 6 8Men 2 10 8
1. What is the probability that a randomly selected person is a woman who likes P.E.?
2. Given that you select a man, what is the probability that he likes Social Studies?
3. What is the probability that you select a person who likes Math?
8/50 = .16
10/20 = .50
18/50 = .36
Skills CheckCorrelation, Linear Regression, & Exponential
Regression
Residuals
From the Carnegie Foundation math.mtsac.edu/statway/lesson_3.3.1_version1.5A
Residuals
Residual is another word for ERROR
Residuals
To find the residual you take the ACTUAL data and SUBTRACT the PREDICTED data.
Analyzing Residuals
Determines the effectiveness of the regression model
Residual Plots
A residual plot is another type of
SCATTERPLOTthat shows the
relationship of the residual to the x value.
Residual Plots Determine
If it 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
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 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 41
37 73
28 54
1.73 0.96y x
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 47.536 56 61.317 27 28.523 35 38.841 65 70.022 41 37.137 73 63.128 54 47.5
1.73 0.96y x
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 -1.928 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?
Total Time
Resi
dual
Good fit or not?
15 20 25 30 35 40 45
-8
-6
-4
-2
0
2
4
6
8
10
12
Total Time
Resi
dual
Classwork
Residuals Task – Carnival
Homework
Residuals CW worksheet
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