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 Fall 2016

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 Fall 2016

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 Fall 2016

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 Fall 2016