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 65 Wife's Height (inches) 60 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 What is the value of a in the new regressio line equation? (round to 2 decimal places)
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 65 Wife's Height (inches) 60 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 What is the value of a in the new regressio line equation? (round to 2 decimal places)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![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:
\[ \hat{W}H_{in} = 40.49 + 0.33HH_{in} \]
where \( \hat{W}H_{in} \) is the wife's height and \( HH_{in} \) is the husband's height. Both are measured in inches.
**Graph Description**:
The scatter plot shows data points representing wife's height (in inches) plotted against husband's height (in inches). The x-axis represents the husband's height, ranging from 60 to 75 inches, and the y-axis represents the wife's height, ranging from 55 to 70 inches. The red line illustrates the least-squares regression line, visually demonstrating the relationship between the two variables.
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:
\[ \hat{W}H_{in} = a + bHH_{cm} \]
**Question**: What is the value of \( a \) in the new regression line equation? (round to 2 decimal places)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f08d3cb-03f2-44ac-afec-90ed33ecc605%2Faf07a984-9322-4c27-a71b-a01a5c81eb49%2Fch7ad9l_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:
\[ \hat{W}H_{in} = 40.49 + 0.33HH_{in} \]
where \( \hat{W}H_{in} \) is the wife's height and \( HH_{in} \) is the husband's height. Both are measured in inches.
**Graph Description**:
The scatter plot shows data points representing wife's height (in inches) plotted against husband's height (in inches). The x-axis represents the husband's height, ranging from 60 to 75 inches, and the y-axis represents the wife's height, ranging from 55 to 70 inches. The red line illustrates the least-squares regression line, visually demonstrating the relationship between the two variables.
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:
\[ \hat{W}H_{in} = a + bHH_{cm} \]
**Question**: What is the value of \( a \) in the new regression line equation? (round to 2 decimal places)
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