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To Compute and Interpret the Correlation Coefficient

 

Example:  In the table below, columns 2 and 3 represent the per capita gross domestic product (in thousands of U.S. dollars) and the average life expectancy of the population, for randomly selected countries in Western Europe.  Compute and interpret the linear correlation coefficient.

 

 

 

Country

 

Per

Capita

GDP,

 

Life

Expectancy,

 

 

 

 

 Austria

21.4

77.48

 21.4 - 21.52

1.531738301

= -0.0783524 

77.48  – 77.754

0.794847295

= -0.34472

(-0.0783424)

(-0.34472)

= 0.027006

 Belgium

23.2

77.53

1.0967931

-0.28182

-0.30909

Finland

20.0

77.32

-0.9923366

-0.54602

0.541832

France

22.7

78.63

0.7703666

1.102098

0.84902

Germany

20.8

77.17

-0.4700542

-0.73473

0.345364

Ireland

18.6

76.39

-1.9063309

-1.71605

3.271365

Italy

21.5

78.51

-0.0130571

0.951126

-0.01242

Netherlands

22.0

78.15

0.3133695

0.498209

0.156123

Switzerland

23.8

78.99

1.4885049

1.555016

2.314648

United

Kingdom

21.2

77.37

-0.2089130

-0.48311

0.100928

 

Press STAT, highlight 1: Edit and clear L1 and L2. Enter the values of the predictor variable (per capita GDP) into L1 and the values of the response variable (life expectancy) into L2. In order to calculate r, the correlation coefficient, you must turn On the Diagnostic command. Press 2nd  (Note: CATALOG is found above the 0 key). The CATALOG of functions will appear on the screen. Use the down arrow to scroll to the DiagnosticOn command.

 

 

Press ENTER ENTER.

 

Press STAT, highlight CALC, select 4:LinReg(ax+b) and press ENTER ENTER. (Note: This command requires that you specify which lists contain the X-values and Y-values. If you do not specify these lists, the defaults are used. The defaults are: L1 for the X-values and L2 for the Y-values.)

 

 

The correlation coefficient is r = .8094195065. This suggests a strong positive linear correlation between X and Y.