CHAPTER 4: TWO VARIABLE ANALYSIS E Spring

Two-variable Analysis  Scatter plot  Covariance  Correlation coefficient  Least squares line

Scatter Plot  Collection of points: first step to analyze two variable relationships  Excel: Highlight two columns of data >> “Insert” menu>> “Scatter” button

Covariance  Measure of the strength of a linear relationship between two variables (direction)  Positive covariance  Positive linear relationship  Negative covariance  Negative linear relationship  Zero covariance  No linear relationship Population Covariance (=COVARIANCE.P(array 1, array 2)) Sample Covariance (=COVARIANCE.S(arra y 1, array 2)) Relation

Correlation coefficient  Unit-free measure of linear relationship (strength)  Excel: =CORREL(array1, array 2)  The higher the correlation coefficient in absolute value, the stronger the relationship: Population Correlation Sample Correlation

Least squares line  Unique line that describes the relationship between two variables, when one has been determined to cause the other.  Excel: “Add trendline” by right clicking the scatter plot. Check “display equation on Chart.”