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Chapter 3: Q 25. (page 174)

Rank the correlations Consider each of the following relationships: the heights of fathers and the heights of their adult sons, the heights of husbands and the heights of their wives, and the heights of women at age 4 and their heights at age 18. Rank the correlations Page Number: 174between these pairs of variables from largest to smallest. Explain your reasoning.

Short Answer

Expert verified

Women at age 4 and 18 has the largest correlations, then the heights of fathers and sons and the last correlation which has the smallest correlation among them is husbands and their wives.

Step by step solution

01

Given information

The heights of women at age 4 and their heights at age 18

02

Explanation

The greatest link exists between women's height at age four and their height at age eighteen, because it is self-evident that as a person becomes older, he or she will grow taller. The father and their adult sons would be the next with the highest correlation. Tall fathers have taller sons. The sons may or may not be as tall as their father, but they will be tall. The relationship between husbands and spouses has the lowest correlation. In general, husbands are taller than their spouses, but there is no association between the two.

Thus, Women at age 4 and 18 has the largest correlations, then the heights of fathers and sons and the last correlation which has the smallest correlation among them is husbands and their wives.

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Most popular questions from this chapter

A school guidance counselor examines how many extracurricular activities students participate in and their grade point average. The guidance counselor says, “The evidence indicates the correlation between the number of extracurricular activities. a student participates in and his or her grade point average is close to 0.” Which of the following is the most appropriate conclusion?

a. Students involved in many extracurricular activities tend to be students with poor grades.

b. Students with good grades tend to be students who are not involved in many extracurricular activities.

c. Students involved in many extracurricular activities are just as likely to get good grades as bad grades.

d. Students with good grades tend to be students who are involved in many

extracurricular activities.

e. No conclusion should be made based on the correlation without looking at a scatterplot of the data.

Teaching and research A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says, “The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero.” The paper reports this as “Professor McDaniel said that good researchers tend to be poor teachers, and vice versa.” Explain why the paper’s report is wrong. Write a statement in plain language (don’t use the word correlation) to explain the psychologist’s meaning.

Longer strides In Exercise 43, we summarized the relationship between x =

height of a student (in inches) and y = number of steps required to walk the length of a school hallway, with the regression line y^=113.6−0.921x. For this

model, technology gives s = 3.50 and r2 = 0.399.

a. Interpret the value of s.

b. Interpret the value of r2.

Sarah’s parents are concerned that she seems short for her age. Their doctor has kept the following record of Sarah’s height:

a. Make a scatterplot of these data using age as the explanatory variable. Describe what you see.

b. Using your calculator, find the equation of the least-squares regression line.

c. Calculate and interpret the residual for the point when Sarah was 48 months old.

d. Would you be confident using the equation from part (b) to predict Sarah’s height when she is 40 years old? Explain.

Actual consumption Refer to Exercise 48. Use the equation of the least-squares regression line and the residual plot to estimate the actual fuel consumption of the car when driving 20 kilometers per hour.
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