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Chapter 4 (Sp11)

# Chapter 4 (Sp11) - Section 4.1 Scatter Diagrams and...

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Section 4.1 – Scatter Diagrams and Correlation Correlation – There is a correlation between two variables when one of them is related to the other in some way. The response variable is the variable whose value can be explained by the value of the predictor (explanatory) variable . Scatter Diagram – A graph in which the (biviariate) paired ( x , y ) sample data are plotted as single points. Each individual in the data set is represented by a single point. The explanatory variable is plotted on the horizontal axis and the response variable is plotted on the vertical axis. Example : Create a scatterplot of the following data: Looking at a scatter diagram can help you determine if the variables have a linear relationship. (See the graphs on pg. 194) The linear correlation coefficient ( r ) measures the strength and direction of the linear relationship between the two variables. It is also called the Pearson product moment correlation coefficient. - - - = 2 2 2 2 ) ( ) ( ) ( ) ( ) )( ( y y n x x n y x xy n r ( ALWAYS ROUND TO 3 DECIMAL PLACES ) x y 3 3 4 2 3 4 1 5 5 2 2 5 5 1 1

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Properties of r : 1. –1 ≤ r ≤ 1 2. The closer r is to +1, the stronger is the evidence of positive association. 3. The closer r is to –1, the stronger is the evidence of negative association.
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