286 Chapter 9 Correlation and Regression
9.8 Assume that a set of data contains a slightly curvilinear relationship between Xand Y(the
best-fitting line is slightly curved). Would it ever be appropriate to calculate ron these data?
9.9 An important developmental question concerns the relationship between severity of cere-
bral hemorrhage in low-birthweight infants and cognitive deficit in the same children at age
5 years.
a. Suppose we expect a correlation of .20 and are planning to use 25 infants. How much
power does this study have?
b. How many infants would be required for power to be .80?
9.10 From the data in Exercise 9.1, compute the regression equation for predicting the percent-
age of births of infants under 2500 grams (Y) on the basis of fertility rate for females
younger than 18 or older than 34 years of age ( ). ( is known as the “high-risk fertility
rate.”)
9.11 Calculate the standard error of estimate for the regression equation from Exercise 9.10.
9.12 Calculate confidence limits on for Exercise 9.10.
9.13 If as a result of ongoing changes in the role of women in society, the age at which women
tend to bear children rose such that the high-risk fertility rate defined in Exercise 9.10
jumped to 70, what would you predict for incidence of babies with birthweights less than
2500 grams? (Note: The relationship between maternal age and low birthweight is particu-
larly strong in disadvantaged populations.)
9.14 Should you feel uncomfortable making a prediction if the rate in Exercise 9.13 were 70?
Why or why not?
9.15 Using the information in Table 9.2 and the computed coefficients, predict the score for
log(symptoms) for a stress score of 8.
9.16 The mean stress score for the data in Table 9.3 was 21.467. What would your prediction for
log(symptoms) be for someone who had that stress score? How does this compare to?
9.17 Calculate an equation for the 95% confidence interval in for predicting psychological
symptoms—you can overlay the confidence limits on Figure 9.2.
9.18 Within a group of 200 faculty members who have been at a well-known university for less
than 15 years (i.e., since before the salary curve levels off) the equation relating salary (in
thousands of dollars) to years of service is 5 0.9X 1 15. For 100 administrative staff at
the same university, the equation is 5 1.5X 1 10. Assuming that all differences are signif-
icant, interpret these equations. How many years must pass before an administrator and a
faculty member earn roughly the same salary?
9.19 In 1886, Sir Francis Galton, an English scientist, spoke about “regression toward medioc-
rity,” which we more charitably refer to today as regression toward the mean. The basic
principle is that those people at the ends of any continuum (e.g., height, IQ, or musical abil-
ity) tend to have children who are closer to the mean than they are. Use the concept of ras
the regression coefficient (slope) with standardized data to explain Galton’s idea.
9.20 You want to demonstrate a relationship between the amount of money school districts spend
on education, and the performance of students on a standardized test such as the SAT. You
are interested in finding such a correlation only if the true correlation is at least .40. What
are your chances of finding a significant sample correlation if you have 30 school districts?
9.21 In Exercise 9.20 how many districts would you need for power 5 .80?
9.22 Guber (1999) actually assembled the data to address the basic question referred to in Exer-
cises 9.20 and 9.21. She obtained the data for all 50 states on several variables associated
with school performance, including expenditures for education, SAT performance, percent-
age of students taking the SAT, and other variables. We will look more extensively at these
data later, but the following table contains the SPSS computer printout for Guber’s data.YNYNYNYb*X 1 X 1