1. 3.2 (part 2)

4. An Example
Test 1
Test 2
Student 1
83.73
90.57
Student 2
88.8
74.59
Student 3
82.65
76.23
Student 4
75.42
69.67
Let’s use scores on the chapter 1 test to predict scores on the chapter 2 test
First step: we need to find the mean and st. dev for each variable

5. An Example
Test 1
Test 2
Student 1
83.73
90.57
Student 2
88.8
74.59
Student 3
82.65
76.23
Student 4
75.42
69.67
First step: we need to find the mean and st. dev for each variable
Test 1
𝑥 =82.65
𝑠 𝑥 =5.52
Test 2
𝑥 =77.77
𝑠 𝑥 =8.98

6. An Example Second step: we need to find the correlation
Test 1
Test 2
Student 1
83.73
90.57
Student 2
88.8
74.59
Student 3
82.65
76.23
Student 4
75.42
69.67 𝑥
77.77
𝑠 𝑥
5.52
8.98
Second step: we need to find the correlation
For now, I’m just going to give it to you: r=.36
Now we can find the slope:
𝑏=(.36)
𝑏=.59

7. An Example Now we can find the y-intercept 𝑎=77.77− .59 82.65 𝑎=28.94
Test 1
Test 2
Student 1
83.73
90.57
Student 2
88.8
74.59
Student 3
82.65
76.23
Student 4
75.42
69.67 𝑥
77.77
𝑠 𝑥
5.52
8.98
Now we can find the y-intercept
𝑎=77.77−
𝑎=28.94
So our regression equation is:
𝑇𝑒𝑠𝑡2 = (𝑇𝑒𝑠𝑡1)
r=.36 b=.59

8. An Example So our regression equation is: 𝑇𝑒𝑠𝑡2 =28.94+.59(𝑇𝑒𝑠𝑡1)
Test 1
Test 2
Student 1
83.73
90.57
Student 2
88.8
74.59
Student 3
82.65
76.23
Student 4
75.42
69.67 𝑥
77.77
𝑠 𝑥
5.52
8.98
So our regression equation is:
𝑇𝑒𝑠𝑡2 = (𝑇𝑒𝑠𝑡1)
A fifth student got a on the Chapter 1 Test. What would we expect his/her grade to be on the chapter 2 test?
r=.36 b=.59

9. An Example So our regression equation is: 𝑇𝑒𝑠𝑡2 =28.94+.59(𝑇𝑒𝑠𝑡1)
Test 1
Test 2
Student 1
83.73
90.57
Student 2
88.8
74.59
Student 3
82.65
76.23
Student 4
75.42
69.67 𝑥
77.77
𝑠 𝑥
5.52
8.98
So our regression equation is:
𝑇𝑒𝑠𝑡2 = (𝑇𝑒𝑠𝑡1)
A fifth student got a on the Chapter 1 Test. What would we expect his/her grade to be on the chapter 2 test?
28.94+(.59)(79.04)
We would expect him/her to get a 75.57
r=.36 b=.59

10. An Example Let’s do the same thing on our calculator
Test 1
Test 2
Student 1
83.73
90.57
Student 2
88.8
74.59
Student 3
82.65
76.23
Student 4
75.42
69.67 𝑥
77.77
𝑠 𝑥
5.52
8.98
Let’s do the same thing on our calculator
Enter our x-values (Test1 scores) into L1 and our y-values (Test2 scores) into L2
𝑇𝑒𝑠𝑡2 = (𝑇𝑒𝑠𝑡1)

11. An Example Let’s do the same thing on our calculator
Test 1
Test 2
Student 1
83.73
90.57
Student 2
88.8
74.59
Student 3
82.65
76.23
Student 4
75.42
69.67 𝑥
77.77
𝑠 𝑥
5.52
8.98
Let’s do the same thing on our calculator
Enter our x-values (Test1 scores) into L1 and our y-values (Test2 scores) into L2
Stat---Calc---Linreg(a+bx)
𝑇𝑒𝑠𝑡2 = (𝑇𝑒𝑠𝑡1)

12. An Example Let’s do the same thing on our calculator
Test 1
Test 2
Student 1
83.73
90.57
Student 2
88.8
74.59
Student 3
82.65
76.23
Student 4
75.42
69.67 𝑥
77.77
𝑠 𝑥
5.52
8.98
Let’s do the same thing on our calculator
Stat---Calc---Linreg(a+bx)
A=29.92
B=.58
Notice: very similar to our equation
Why is it a bit different?
𝑇𝑒𝑠𝑡2 = (𝑇𝑒𝑠𝑡1)

13. A New Example: Stadium Size
Stadium Size (thousands)
2016 Win Pct
Texas
100.1
.417
Old Dominion
20.1
.769
Auburn
87.5
.615
Hawaii
50.0
.500
Kansas
50.1
.167
Colorado
50.2
.714
Colorado State
41.2
.538
Using your calculator, find the regression line that uses stadium size to predict 2016 Winning Percentage
Use the regression line to predict the 2016 winning percentage for Tulane (stadium seats 30,000)

14. A New Example: Stadium Size
Stadium Size (thousands)
2016 Win Pct
Texas
100.1
.417
Old Dominion
20.1
.769
Auburn
87.5
.615
Hawaii
50.0
.500
Kansas
50.1
.167
Colorado
50.2
.714
Colorado State
41.2
.538
Using your calculator, find the regression line that uses stadium size to predict 2016 Winning Percentage
𝑤𝑖𝑛 =.654−.002(Stadium)
Use the regression line to predict the 2016 winning percentage for Tulane (stadium seats 30,000)
.594

15. A New Example: Stadium Size
Stadium Size (thousands)
2016 Win Pct
Texas
100.1
.417
Old Dominion
20.1
.769
Auburn
87.5
.615
Hawaii
50.0
.500
Kansas
50.1
.167
Colorado
50.2
.714
Colorado State
41.2
.538
𝑤𝑖𝑛 =.654−.002(Stadium)
Use the regression line to predict the 2016 winning percentage for Tulane (stadium seats 30,000)
.594
Tulane’s actual winning percentage last year was Did our model do a very good job of predicting this?

18. No Pattern—Good!

19. Residual Plots What if the residual plot DOES have a pattern?
Linear regression is probably not appropriate
For now, we just stop there
There are non-linear regression methods (your calculator can even do some of them)
But for now we are focused only on linear regression

20. Using Technology—making a scatterplot
We still have these data in L1 and L2 of our calculator
We can use L1 and L2 to make a scatterplot
Go to Y= and delete any equations you have in there
Go to 2nd—Stat plot

21. Using Technology—making a scatterplot
Go to Y= and delete any equations you have in there
Go to 2nd—Stat plot
Turn Plot1 on (make sure you choose L1 and L2)
Hit Graph—you will probably see no points. Why?

22. Using Technology—making a scatterplot
Hit Graph—you will probably see no points. Why?
Click Window—change xmin, xmax, ymin, and ymax
Now let’s add our regression line: 𝑤𝑖𝑛 =.654−.002(Stadium)

23. Using Technology—Making a Residual Plot (Page 178)
Go to Stat---Edit
Leave data in L1 and L2
Scroll over to L3 and highlight “L3”
Type: .654− .002∗𝐿1
Now L3 is holding predicted values
Now highlight “L4”
Type: L2-L3
Now L4 is holding residuals
Go back to Stat Plot
Turn Plot 1 off, and turn plot 2 on
Specify L1 as X variable, and L4 as y-variable
Go to Window and change ymin (-1 works in this case)
Go to Y= and delete your regression line (or hide it)
Hit graph

24. HW Time