Session 12_Corr&Regression Analysis.pptx

Session 12_Corr&Regression Analysis.pptx - CORRELATION...

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CORRELATION ANALYSIS
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Summarizing Bivariate Data (Two Variables) Using Graphical Displays In most cases, a graphical display is more useful than a table for recognizing patterns and trends. Scatter diagrams and trend lines are useful in exploring the relationship between two variables. Scatter diagram It is a graphical presentation of the relationship between two quantitative variables One variable is shown on the horizontal axis and the other variable is shown on the vertical axis. The general pattern of the plotted points suggests the overall relationship between the variables. A trend line provides an approximation of the relationship.
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Scatter Diagram A Positive Relationship x y
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Scatter Diagram A Negative Relationship x y
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Scatter Diagram No Apparent Relationship x y
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Example: Panthers Football Team 1 3 2 1 3 14 24 18 17 30 x = Number of Interceptions y = Number of Points Scored Scatter Diagram The Panthers football team is interested in investigating the relationship, if any, between interceptions made and points scored.
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Scatter Diagram and Trend line y x Number of Interceptions Number of Points Scored 5 10 15 20 25 30 0 35 1 2 3 0 4
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Insights Gained from the Preceding Scatter Diagram The relationship is not perfect; all plotted points in the scatter diagram are not on a straight line. Higher points scored are associated with a higher number of interceptions. The scatter diagram indicates a positive relationship between the number of interceptions and the number of points scored. Example: Panthers Football Team
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Measures of Association Between Two Variables So far we have examined numerical methods used to summarize the data for one variable at a time Often a manager or decision maker is interested in the relationship between two variables. Two descriptive measures of the relationship between two variables are covariance and correlation coefficient.
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Covariance The covariance is a measure of the linear association between two variables Positive values indicate a positive relationship Negative values indicate a negative relationship.
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