Covariance/ Correlation

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. 123-126)

2
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
74 87
65 78
83 90
Data Analysis - correlation
  Math grade English grade
Math grade 1
English grade 0.2396 1
3
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 28.2216 0.243756 0.647387
Residual 4 463.1117 115.7779
Total 5 491.3333      
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 0.239663917
• The R value further supports the concept that
  Math Grades and English grades are not correlated.