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. 123-126) JMB Chapter 4 Lecture 2 9th ed EGR 252 2013
Calculating Correlation Using Sample Data Statistical software is often used to calculate the sample correlation coefficient (r) Exercise 11.43 – 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 252 2013
Calculating Correlation Using Sample Data Exercise 11.43 on page 435 continued Data Analysis - regression Regression Statistics Multiple R 0.239663917 ANOVA df SS MS F Significance F Regression 1 28.2216 0.243756 0.647387 Residual 4 463.1117 115.7779 Total 5 491.3333 JMB Chapter 4 Lecture 2 9th ed EGR 252 2013
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 0.239663917 The R value further supports the concept that Math Grades and English grades are not correlated. JMB Chapter 4 Lecture 2 9th ed EGR 252 2013