Chapter 16, Problem 11P

Ii. Problem 13 in Chapter 15 examined the relationship between weight and income for a sample of $n=8$ men. Weights were classified in five categories and had a mean of $M=\text{3}$ with $SS=\text{18}$ . Income, measured in thousands, had a mean score of $M=\text{88}$ with $SS=\text{21}.\text{6}0\text{9}$ , and $SP=\text{33}0$ .

a. Find the regression equation for predicting income from weight. (Identify the weight scores as X values and the income scores as Y values.)

b. What percentage of the variance in the income is accounted for by the regression equation? (Compute the correlation, r, then find $r^2$ .)

c. Does the regression equation account for a significant portion of the variance in income? Use $\alpha =.05$ to evaluate the F-ratio.

The researchers cited in the previous problem also examined the weight/salary relationship for men and found a positive relationship, suggesting that we have very different standards for men than for women (Judge & Cable, 2010). The following are data similar to those obtained for a sample of male professionals. Again, weight relative to height is coded in five categories from 1 = thinnest to 5 = heaviest. Income is recorded as thousands earned annually.

a. Calculate the Person correlation for these data.

b. Is the correlation statistically significant? Use a two-tailed test with $\alpha =.05$ .

X

Y

4
151
3
52
3
52
2
73
1
49
3
92
1
56
5
143