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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 |
Life |
|
|
|
|
Austria |
21.4 |
77.48 |
21.4 - 21.52 1.531738301 = -0.0783524 |
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.