1. 3.2 (part 1)

4. Y-hat
Why do we label the predicted value y-hat instead of just y?

5. Y-hat Why do we label the predicted value y-hat instead of just y?
Because the “true” y values are just labeled as y
So “true” or “observed” y values are just y
“Predicted” y values are y-hat

6. GPA Example GPA Stats Grade Student 1 3.317 94.37 Student 2 2.500
76.06
Student 3
4.024
100.73
Student 4
4.238
97.11

7. GPA Example When I calculate a regression line, I get:
𝐺𝑟𝑎𝑑𝑒 = (𝐺𝑃𝐴)
GPA
Stats Grade
Student 1
3.317
94.37
Student 2
2.500
76.06
Student 3
4.024
100.73
Student 4
4.238
97.11

8. GPA Example When I calculate a regression line, I get:
𝐺𝑟𝑎𝑑𝑒 = (𝐺𝑃𝐴)
So if I want to estimate (or predict) the grade in AP Stats for someone with a 3.12 GPA, what would I do?
GPA
Stats Grade
Student 1
3.317
94.37
Student 2
2.500
76.06
Student 3
4.024
100.73
Student 4
4.238
97.11

9. GPA Example When I calculate a regression line, I get:
𝐺𝑟𝑎𝑑𝑒 = (𝐺𝑃𝐴)
So if I want to estimate (or predict) the grade in AP Stats for someone with a GPA, what would I do?
𝐺𝑟𝑎𝑑𝑒 =
So our predicted grade is
GPA
Stats Grade
Student 1
3.317
94.37
Student 2
2.500
76.06
Student 3
4.024
100.73
Student 4
4.238
97.11

10. Practice (Corvettes)
𝑃 =371.6−27.9(𝐴𝑔𝑒)
Use the regression equation to predict the value of a brand new Corvette
Predict the value of a 3 year old Corvette
Predict the value of a 20 year old Corvette

11. Practice (Corvettes)
Note: Price in hundreds of dollars
𝑃 =371.6−27.9(𝐴𝑔𝑒)
Use the regression equation to predict the value of a brand new Corvette $37,160
Predict the age of a 3 year old Corvette $28,790
Predict the age of a 20 year old Corvette $18,640
Someone will PAY YOU to take their 20 year old Corvette!!!!!!

12. Extrapolation

13. Residuals

14. Positive and Negative Residuals
So if a positive residual is above the line, that means that 𝑦> 𝑦
Or in other words, the model UNDERpredicted for that value of x
If the residual is below the line, it is negative
So 𝑦< 𝑦
The model OVERpredicted for that value of x

15. Residuals Practice So 𝐺𝑟𝑎𝑑𝑒 =46.73+12.88(𝐺𝑃𝐴)
Find residuals for each student Y 𝒚
Residual
U/O
Student 1
94.37
89.45
4.92
Under-Predicted
Student 2
76.06
78.93
-2.87
Over
Student 3
100.73
98.56
2.17
Under
Student 4
97.11
101.32
-4.21

16. Next Class We will learn how to actually calculate the regression line
You’ve done this before on your calculaltors
We will learn ways to assess whether linear regression is appropriate for the situation
And we will learn how to assess how well the model is doing at predicting the outcome variable
Can compare which predictor is more effective