1. Covariance/ Correlation
A measure of the nature of the association between two variables
Describes a potential linear relationship
Positive relationship
Large values of X result in large values of Y
Negative relationship
Large values of X result in small values of Y
“Manual” calculations are based on the joint probability distributions
See examples in Chapter 4 (pp )
JMB Chapter 4 Lecture 2 9th ed
EGR

2. Calculating Correlation Using Sample Data
Statistical software is often used to calculate the sample correlation coefficient (r)
Exercise – data on page 435
Math grade
English grade 70 74 92 84 80 63 87 65 78 83 90
Data Analysis - correlation
Math grade
English grade 1
0.2396
JMB Chapter 4 Lecture 2 9th ed
EGR

3. Calculating Correlation Using Sample Data
Exercise on page 435 continued
Data Analysis - regression
Regression Statistics
Multiple R
ANOVA df SS MS F
Significance F
Regression 1
Residual 4
Total 5
JMB Chapter 4 Lecture 2 9th ed
EGR

4. Calculating Correlation Using Sample Data
It is important to graph data BEFORE conducting linear regression in Excel.
The graphs suggest that linear regression is not a good model.
Regression Statistics
Multiple R
The R value further supports the concept that Math Grades and English grades are not correlated.
JMB Chapter 4 Lecture 2 9th ed
EGR