/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 63. Husbands and wives The mean heig... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q 63. (page 207)

Husbands and wives The mean height of married American women in their

early 20s is 64.5 inches and the standard deviation is 2.5 inches. The mean height of married men the same age is 68.5 inches with standard deviation 2.7 inches. The correlation between the heights of husbands and wives is about r = 0.5.

a. Find the equation of the least-squares regression line for predicting a husband鈥檚 height from his wife鈥檚 height for married couples in their early 20s.

b. Suppose that the height of a randomly selected wife was 1 standard deviation below average. Predict the height of her husband without using the least-squares line.

Short Answer

Expert verified

Part (a)y铃�=33.67+0.54x

Part (b)67.15inches.

Step by step solution

01

Part (a) Step 1: Given information

r=0.5x=64.5sx=2.5y=68.5sy=2.7

02

Part (a) Step 2: Explanation

The general equation of the regression line is:

y铃�=a+bx

The slope of the regression line is:

b=rsysx=0.5脳2.72.5=0.54

And the intercept is as:

a=y鈭�bx=68.5鈭�0.54(64.5)=33.67

Thus, the equation of the regression line is:

y铃�=a+bx=33.67+0.54x

03

Part (b) Step 1: Explanation

As a result, by noting that the wife's height is one standard deviation below the mean for women and that the man's expected height must match the correlation coefficient's product and the standard deviation below the mean, we can intuitively arrive at a solution:

y铃�=y+rsy=68.5鈭�0.5(2.7)=67.15

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Hot dogs Are hot dogs that are high in calories and also high in salt? The

following scatterplot shows the calories and salt content (measured in milligrams of sodium) in 17 brands of meat hot dogs.

a. The correlation for these data is r=0.87 Interpret this value.

b. What effect does the hot dog brand with the smallest calorie content have on the correlation? Justify your answer.

More brains Refer to Exercise 20

a. Explain why it isn鈥檛 correct to say that the correlation is 0.86g/kg

b. What would happen to the correlation if the variables were reversed on the scatterplot?

Explain your reasoning.

c. What would happen to the correlation if brain weight was measured in kilograms instead of grams? Explain your reasoning.

The stock market Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable xto be the percent change in a stock market index in January and the response variable yto be the change in the index for the entire year. We expect a positive correlation between xand y because the change during January contributes to the full year鈥檚 change. Calculation from data for an 18-year period gives

x炉=1.75%sz=5.36%y炉=9.07%sy=15.35%r=0.596

(a) What percent of the observed variation in yearly changes in the index is explained by a straight-line relationship with the change during January?

(b) For these data, s=8.3Explain what this value means

IQ and grades Exercise 3 (page 158) included the plot shown below of school grade point average (GPA) against IQ test score for 78seventh-grade students. (GPA was recorded on a 12-point scale with A+=12,A=11,A-=10,B+=9,...D-=1,F=0.) Calculation shows that the mean and standard deviation of the IQ scores areX炉=108.9and Sx=13.17For the GPAs, these values are Y=7.447andSy=2.10. The correlation between IQ and GPA is 0.6337

(a) Find the equation of the least-squares line for predicting GPA from IQ. Show your work.

(b) What percent of the observed variation in these students鈥� GPAs can be explained by the linear relationship between GPA and IQ?

(c) One student has an IQ of 103but a very low GPA of 0.53. Find and interpret the residual for this student

Which of the following is not a characteristic of the least-squares regression line?

a. The slope of the least-squares regression line is always between 鈥�1 and 1.

b. The least-squares regression line always goes through the point (x炉,y炉) .

c. The least-squares regression line minimizes the sum of squared residuals.

d. The slope of the least-squares regression line will always have the same sign as the correlation.

e. The least-squares regression line is not resistant to outliers.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.