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CHAPTER 18- COMPLEX STATISTICS

CORRELATIONWhat is it? A relationship or association between two variables.

STRENGTH

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 73 68 75 78 73 77 84 86

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.

MEASURING CORRELATION

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

PEARSON’S CORRELATION COEFFICIENT

•

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

COEFFICIENT OF DETERMINATION

Value Strength of Associationr2 = 0 No correlation0 < 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 correlationr2 = 1 Perfect correlation

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 3

C 4 6

D 5 8

x y xy x2 Y2

1 32 34 65 8

12 20

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 6 4

D 3 6

E 9 3

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 13.23 and the covariance of x and y is -9.26

• ∑x = 65, ∑y = 141, ∑xy = 1165, ∑x2 = 505,

∑y2 = 2745 , n = 11