1. Announcements
Turn in homework Papers galore- Exams, homework, project proposal, etc. WILL GET IT ALL WEDNDESDAY. IB Grades New Layered Assessment Posted Criteria A and B due next Thursday!!! Get a graphing calculator!!!

2. Chapter 18- Complex Statistics

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

4. Strength

5. 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 negative. (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

6. 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.

7. 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

8. 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

9. 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

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. Find the correlation if..
Sx = 14.7, sy = 19.2 and sxy = 136.8
The standard deviation of the x distribution is 8.71, the standard deviation of y is and the covariance of x and y is -9.26
∑x = 65, ∑y = 141, ∑xy = 1165, ∑x2 = 505,
∑y2 = 2745 , n = 11