1. How to find the regression line of a scatter plot using Mayer’s Method

2. Quick Review STRONG POSITIVE
What kind of correlation do we have here? Positive or negative? Weak or strong?

3. STRONG: The points are close together and almost form a line
POSITIVE: Y increases as X increases

4. Time spent studying (hours) Results on final exam (%)
Can we find the rule of this situation? Is there a rule of the form y = ax + b that can describe the situation?
Time spent studying (hours)
Results on final exam (%)
0,5 30 40 1 50 95
1,5 60 65 2
2,5 75 3 80 90
3,5 70 4
4,5 85 5
100 6
+ 0,5
+ 10
+ 0,5
+ 20
ANSWER: No, we can’t.

5. What if we wanted to find a rule that could help us predict, give us an idea of what our values would be? Would that be possible?
ANSWER: Yes, it would be possible!

6. How can I find the rule of this line?
Using MAYER’S METHOD

7. Time spent studying (hours) Results on final exam (%)
Mayer’s Line
Time spent studying (hours)
Results on final exam (%)
0,5 30 40 1 50 95
1,5 60 65 2
2,5 75 3 80 90
3,5 70 4
4,5 85 5
100 6
Step 1:
Order the ordered pairs in the distribution according to their x-coordinates.

8. Time spent studying (hours) Results on final exam (%)
0,5 30 40 1 50 95
1,5 60 65 2
2,5 75 3 80 90
3,5 70 4
4,5 85 5
100 6
Step 2:
Divide the ordered pairs into two equal group if possible*.
9 ordered pairs
9 ordered pairs
*We will later see how to apply the method with an odd number of ordered pairs.

9. Time spent studying (hours) Results on final exam (%)
0,5 30 40 1 50 95
1,5 60 65 2
2,5 75 3 80 90
3,5 70 4
4,5 85 5
100 6
Step 3:
Determine the average of the x-coordinates and the average of the y-coordinates in each of the two groups. This will give you your P1 and your P2.
X1 = =1.44
Y1 = =60
X2 = =4.22
Y2 = =82.22
P1(x1, y1): (1.44, 60)
P2 (x2, y2): (4.22, 82.22)

10. The regression line is the line that passes through points P1 and P2
Step 4:
The regression line is the line that passes through points P1 and P2
P1(x1, y1): (1.44, 60)
P2 (x2, y2): (4.22, 82.22)
Find a
a = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 = 82.22− −1.44 = =𝟖
2) Find b
𝑦=𝑎𝑥+𝑏
60= 𝑏
60=11.52+𝑏
60−11.52=𝑏
𝟒𝟖.𝟒𝟖=𝑏
Regression Line
𝑦=8𝑥+48.48

11. Now let’s go back to our scatter plot…
𝒚=𝟖𝒙+𝟒𝟖.𝟒𝟖

12. Find the regression line of the following set of data
Now it’s your turn!
Find the regression line of the following set of data
Steps
Make sure all the pairs are ordered according to the x-coordinates.
Divide all the ordered pairs into two equal groups, if possible.
Determine the average of the x-coordinates and the average of the y-coordinates. This is how you get your P1 and P2.
The regression line is the line that passes through P1 and P2. X Y 6 23 7 26 10 39 13 44 14 48 15 55 18 50 19 65 68 25 72

13. ANSWER
𝑦=2.6𝑥+10

14. 𝑦=2.3𝑥+14 Regression Line Now what if we have an odd number of data?
Just put the extra pair in one of the two groups! X Y 6 23 7 26 10 39 13 44 14 48 15 55 18 50 19 65 68 25 72 27 73
6 ordered pairs
Regression Line
𝑦=2.3𝑥+14
5 ordered pairs