Consider data on heights of husbands and wives for a sample of 199 married couples in the UK collected by the Great Britain Office of Population Census and Surveys.[1] The scatter plot below shows wife height plotted against husband height and the least-squares regression line is shown in red. The equation of the regression line is: WÊin = 40.49 + 0.33H Hin where WHin is the wife's height and HHin is the husband's height. Both are measured in inches. 7 Wife's Height (inches) 55 60 65 70 Husband's Height (inches) 75 Now consider a new variable for husband height measured in centimeters called HHcm. Because there are 2.54 cm per inch, this variable is defined as HHcm = 2.54* HHin. Suppose we use the exact same sample, but instead estimate a regression line with husband height in centimeters while wife height is still measured in inches: WHin = a + bHHcm How tall does a husband have to be in inches? Use the original regression equation provided for the regressi to predict that his wife will be the same height. (Round to the nearest whole number)
Consider data on heights of husbands and wives for a sample of 199 married couples in the UK collected by the Great Britain Office of Population Census and Surveys.[1] The scatter plot below shows wife height plotted against husband height and the least-squares regression line is shown in red. The equation of the regression line is: WÊin = 40.49 + 0.33H Hin where WHin is the wife's height and HHin is the husband's height. Both are measured in inches. 7 Wife's Height (inches) 55 60 65 70 Husband's Height (inches) 75 Now consider a new variable for husband height measured in centimeters called HHcm. Because there are 2.54 cm per inch, this variable is defined as HHcm = 2.54* HHin. Suppose we use the exact same sample, but instead estimate a regression line with husband height in centimeters while wife height is still measured in inches: WHin = a + bHHcm How tall does a husband have to be in inches? Use the original regression equation provided for the regressi to predict that his wife will be the same height. (Round to the nearest whole number)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Consider data on heights of husbands and wives for a sample of 199 married couples in the UK collected by the Great Britain Office of Population Census and Surveys. The scatter plot below shows wife height plotted against husband height, and the least-squares regression line is shown in red. The equation of the regression line is:
\[ WH_{in} = 40.49 + 0.33 HH_{in} \]
where \( WH_{in} \) is the wife's height and \( HH_{in} \) is the husband's height. Both are measured in inches.
**Graph Explanation:**
The scatter plot displays individual data points representing the height of wives relative to their husbands' heights, measured in inches. The red line represents the least-squares regression line, demonstrating the trend in the data, where a positive slope indicates a correlation between husband and wife heights.
Now consider a new variable for husband height measured in centimeters called \( HH_{cm} \). Because there are 2.54 cm per inch, this variable is defined as \( HH_{cm} = 2.54 \times HH_{in} \). Suppose we use the exact same sample, but instead estimate a regression line with husband height in centimeters while wife height is still measured in inches:
\[ WH_{in} = a + b HH_{cm} \]
**Problem:**
How tall does a husband have to be in inches? Use the original regression equation provided for the regression to predict that his wife will be the same height. (Round to the nearest whole number)
**Solution:**
To predict that the wife will be the same height as the husband, set \( WH_{in} = HH_{in} \) in the original equation:
\[ HH_{in} = 40.49 + 0.33 HH_{in} \]
Rearrange the equation to solve for \( HH_{in} \):
\[ HH_{in} - 0.33 HH_{in} = 40.49 \]
\[ 0.67 HH_{in} = 40.49 \]
\[ HH_{in} = \frac{40.49}{0.67} \]
\[ HH_{in} \approx 60.43 \]
Thus, the husband needs to be approximately 60 inches tall. Rounding to the nearest whole number, it is 60 inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f08d3cb-03f2-44ac-afec-90ed33ecc605%2Ffbc93b0c-91c7-44cc-b12c-4ef24511e987%2Fd5voojg_processed.png&w=3840&q=75)
Transcribed Image Text:Consider data on heights of husbands and wives for a sample of 199 married couples in the UK collected by the Great Britain Office of Population Census and Surveys. The scatter plot below shows wife height plotted against husband height, and the least-squares regression line is shown in red. The equation of the regression line is:
\[ WH_{in} = 40.49 + 0.33 HH_{in} \]
where \( WH_{in} \) is the wife's height and \( HH_{in} \) is the husband's height. Both are measured in inches.
**Graph Explanation:**
The scatter plot displays individual data points representing the height of wives relative to their husbands' heights, measured in inches. The red line represents the least-squares regression line, demonstrating the trend in the data, where a positive slope indicates a correlation between husband and wife heights.
Now consider a new variable for husband height measured in centimeters called \( HH_{cm} \). Because there are 2.54 cm per inch, this variable is defined as \( HH_{cm} = 2.54 \times HH_{in} \). Suppose we use the exact same sample, but instead estimate a regression line with husband height in centimeters while wife height is still measured in inches:
\[ WH_{in} = a + b HH_{cm} \]
**Problem:**
How tall does a husband have to be in inches? Use the original regression equation provided for the regression to predict that his wife will be the same height. (Round to the nearest whole number)
**Solution:**
To predict that the wife will be the same height as the husband, set \( WH_{in} = HH_{in} \) in the original equation:
\[ HH_{in} = 40.49 + 0.33 HH_{in} \]
Rearrange the equation to solve for \( HH_{in} \):
\[ HH_{in} - 0.33 HH_{in} = 40.49 \]
\[ 0.67 HH_{in} = 40.49 \]
\[ HH_{in} = \frac{40.49}{0.67} \]
\[ HH_{in} \approx 60.43 \]
Thus, the husband needs to be approximately 60 inches tall. Rounding to the nearest whole number, it is 60 inches.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman