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# Coefficient of Determination for AP Statistics (page 2)

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By McGraw-Hill Professional
Updated on Feb 3, 2011

Example: Consider the following output for a linear regression:

We can see that the LSRL for these data is = –1.95 + 0.8863x. r2 = 53.2% = 0.532. This means that 53.2% of the total variability in y can be explained by the regression of y on x. Further, r = = 0.729(r is positive since b = 0.8863 is positive). We learn more about the other items in the printout later.

You might note that there are two standard errors (estimates of population standard deviations) in the computer printout above. The first is the "St Dev of x" (0.2772 in this example). This is the standard error of the slope of the regression line, sb the estimate of the standard deviation of the slope (for information, although you don't need to know this, ). The second standard error given is the standard error of the residuals, the "s" (s = 16.57) at the lower left corner of the table. This is the estimate of the standard deviation of the residuals (again you don't need to know this, ).

Practice problems for these concepts can be found at:

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