37. Correlations with Transformed Data In addition to testing for a linear correlation between x and y, we can often use transformations of data to explore for other relationships.

For example, we might replace each x value by x2 and use the methods of this section to determine whether there is a linear correlation between y and x2. Given the paired data in the accompanying table, construct the scatterplot and then test for a linear correlation between y and each of the following. Which case results in the largest value of r?

a. x

b. x2

c. log x

d. !x

e. 1>x x 1.3 2.4 2.6 2.8 2.4 3.0 4.1 y 0.11 0.38 0.41 0.45 0.39 0.48 0.61 38. Finding Critical r-Values The critical values of r in Table A-6 are found by solving t 5 r

Ç

1 2 r 2 n 2 2 continued 540 Chapter 10 Correlation and Regression for r to get where the t value is found from Table A-3 by assuming a two-tailed case with n  2 degrees of freedom. Table A-6 lists the results for selected values of n and

a. Use the formula for r given here and Table A-3 (with n  2 degrees of freedom) to find the critical values of r for the given cases.

a.

b.

c.

d.

e.