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Correlation and regression analysis are statistical methods used to determine if a relationship exists between variables and describe the nature of that relationship. A scatter plot graphs the independent and dependent variables and allows visualization of any trends in the data. The correlation coefficient measures the strength and direction of the linear relationship between variables, ranging from -1 to 1. Regression finds the linear "best fit" line that minimizes the residuals and can be used to predict dependent variable values.

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Chapter 10: Correlation and Regression
Correlation & Regression ,[object Object],[object Object]
Independent and Dependent Variable ,[object Object],[object Object],[object Object]
Scatter Plot ,[object Object],[object Object]
Analyzing a Scatter Plot ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example: Construct a scatter plot of the data and discuss any trends that you see. ,[object Object],54.4 71.3 44.5 41.6 80.6 52.2 28.7 62.5 Yield of Wheat (bushels per acre) 13.1 15.9 10.3 8.8 18.6 11.3 7.2 12.9 Rainfall (inches)
Example: Prepare a scatter plot of the data and discuss any trends. ,[object Object],[object Object]
Correlation Coefficient ,[object Object],[object Object],[object Object]
Correlation Coefficient (cont’d.) ,[object Object],[object Object],[object Object]
Correlation Coefficient (cont’d.) ,[object Object],Strong negative linear relationship Strong positive linear relationship  1  1 0 No linear relationship
Formula for the Correlation Coefficient r ,[object Object]
Possible Relationships Between Variables ,[object Object],[object Object],[object Object]
Possible Relationships Between Variables ,[object Object],[object Object]
Interpretation of Relationships ,[object Object]
Example ,[object Object],82 80 88 92 93 90 95 Heart Rate, y 0.50 0.40 0.35 0.30 0.25 0.20 0.125 Drug Dosage, x
Example ,[object Object],87 90 83 65 70 90 75 Cost, y 4 6 2 1 3 4 2 Age, x
Steps in Regression Analysis ,[object Object],[object Object],[object Object]
Steps in Regression Analysis ,[object Object]
[object Object],[object Object]
[object Object],[object Object]
[object Object]
[object Object],[object Object]
Example: Drug dosage vs. Heart Rate Data Revisited ,[object Object],[object Object]
Example: Age of Register vs. Repair Cost Data Revisited ,[object Object],[object Object]
The Coefficient of Determination ,[object Object],[object Object]
[object Object],[object Object]
Example ,[object Object]
Example ,[object Object]
 

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Chapter 10

  • 1. Chapter 10: Correlation and Regression
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