1. Get a graphing calculator!!!
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Get a graphing calculator!!!

2. Bellringer- Think about it….
How can you get exactly 4 gallons of water if you have a 5 gallon bucket, a 3 gallon bucket, and a hose with water.

3. Complex Statistics

4. Correlation
What is it? A relationship or association between two variables.

5. Strength

6. 5 Minute CHeck
Construct a scatter plot using the following data. Then state if it has correlation, if it is positive or negative, and if it is strong, weak, or moderate. (MAKE THE SCALES ON BOTH AXES FROM 60-90)
Student A B C D E F G H I
Math Test 64 67 69 70 73 74 77 82 84
Science Test 68 75 78 86

7. NOTE: Correlation is NOT causation
Consider this: Arm Length and Running Speed It was found that amongst a group of children, there was a positive correlation found. Does this mean that short arms cause a reduction in running speed? Or that a high running speed causes your arms to grow long? NO! It is just a relationship, not a CAUSE.

8. Measuring Correlation
The strength of a relationship is best measured by the correlation coefficient (r).
An r value of 0 suggests there is no correlation
A value of 1 suggests a perfect positive correlation
A value of -1 suggests a perfect negative correlation

9. Pearson’s correlation coefficient
𝑟= 𝑥 − 𝑥 (𝑦− 𝑦) (𝑥− 𝑥 ) (𝑦− 𝑦 ) 2
𝑟= 𝑠 𝑥𝑦 𝑠 𝑥 𝑠 𝑦
𝑟= 𝑥𝑦 −𝑛 𝑥 𝑦 𝑥 2 −𝑛 𝑥 𝑦 2 −𝑛 𝑦 2

10. Coefficient of Determination
Value
Strength of Association
r2 = 0
No correlation
0 < r2 < .25
Very weak correlation
.25 ≤ r2 < .50
Weak correlation
.50 ≤ r2 < .75
Moderate correlation
.75 ≤ r2 < .90
Strong correlation
.90 ≤ r2 < 1
Very strong correlation
r2 = 1
Perfect correlation

11. Practice Problem 1
A chemical fertilizer company wishes to determine the extent of correlation between ‘quantity of compound X used’ and ‘lawn growth’ per day. Find Pearson’s correlation coefficient between the two variables.
Lawn
Compound X (g)
Lawn Growth (mm) A 1 3 B 2 C 4 6 D 5 8

12. x y xy x2 Y2 1 3 2 4 6 5 8 12 20

13. Number of surviving lawn beetles
Practice Problem 2
Wydox have been trying out a new chemical to control the number of lawn beetles in the soil. Determine the extent of the correlation between the quantity of chemical used and the number of surviving lawn beetles per square meter of lawn.
Lawn
Amount of chemical (g)
Number of surviving lawn beetles A 2 11 B 5 6 C 4 D 3 E 9

14. Bellringer

15. Find the correlation if..
Sx = 14.7, sy = 19.2 and sxy = 136.8

16. Practice

17. Put data in List 1 and List 2 Stat- Tests- E: LinRegTTest- Enter
Technolgoy
Put data in List 1 and List 2
Stat- Tests- E: LinRegTTest- Enter
X List: List 1, Y List: List 2, Calculate
Scroll down to r

18. Example

19. Practice

20. With your data… Create a scatter plot Find the correlation by hand.
Find the correlation by calculator. See if they match up.
Conclusion: Describe the association between your two variables. This should be a paragraph.
What you don’t finish will be homework.