Question

The height of bedridden patients is often estimated from the length of the patient's ulna, the distance between the point on the elbow and the prominent bone on the wrist. Eight men over the age of 65 had both their height (in centimeters) and the length of their ulna (in centimeters) measured. The data are given in the table below. Ulna length (cm) 20 23 24 26 27 29 30 31 Height (cm) 160 163 166 168 171 178 182 186 Let x denote a patient's ulna length (in cm) and y denote the patient's height (in cm). Assume that the population distributions for both ulna length and height are approximately normal. The following summary measures were obtained from the data. $\bar{x}$ = 26.25, $\bar{y}$ = 171.75, SSxx = 99.5, SSyy = 609.5, SSxy = 238.5 From the data, the equation of the least squares regression line is $\hat{y}$ = 108.829 + 2.397x. Use the information to calculate the coefficient of determination. Express your answer using three decimal places.

          The height of bedridden patients is often estimated from the length of the patient's ulna, the distance between the point on the elbow
and the prominent bone on the wrist. Eight men over the age of 65 had both their height (in centimeters) and the length of their ulna
(in centimeters) measured. The data are given in the table below.
Ulna length (cm) 20
23
24
26
27
29
30
31
Height (cm)
160
163
166
168
171 178
182
186
Let x denote a patient's ulna length (in cm) and y denote the patient's height (in cm). Assume that the population distributions for both
ulna length and height are approximately normal. The following summary measures were obtained from the data.
$\bar{x}$ = 26.25, $\bar{y}$ = 171.75, SSxx = 99.5, SSyy = 609.5, SSxy = 238.5
From the data, the equation of the least squares regression line is $\hat{y}$ = 108.829 + 2.397x.
Use the information to calculate the coefficient of determination. Express your answer using three decimal places.

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the height of bedridden patients is often estimated from the length of the patients ulna the distance between the point on the elbow and the prominent bone on the wrist eight men over the ag 45039

Added by Jennifer D.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jerelyn Nevil

10/13/2022

Step 1

Step 1: The coefficient of determination, denoted by $R^2$, is the square of the correlation coefficient, $r$. Show more…

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The height of bedridden patients is often estimated from the length of the patient's ulna, the distance between the point on the elbow and the prominent bone on the wrist. Eight men over the age of 65 had both their height (in centimeters) and the length of their ulna (in centimeters) measured. The data are given in the table below. Ulna length (cm) 20 23 24 26 27 29 30 31 Height (cm) 160 163 166 168 171 178 182 186 Let x denote a patient's ulna length (in cm) and y denote the patient's height (in cm). Assume that the population distributions for both ulna length and height are approximately normal. The following summary measures were obtained from the data. $\bar{x}$ = 26.25, $\bar{y}$ = 171.75, SSxx = 99.5, SSyy = 609.5, SSxy = 238.5 From the data, the equation of the least squares regression line is $\hat{y}$ = 108.829 + 2.397x. Use the information to calculate the coefficient of determination. Express your answer using three decimal places.

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00:01 When an anthropologist finds skeletal remains, they need to figure out the height of the person.

00:05 The height of the person in centimeters and the length of a metacarpal bone in centimeters were collected for 22 sets of skeletal remains.

00:13 The data are in the table below.

00:17 So here's the table of the data.

00:20 And so it says find the equation of the best fitting line, the least squares regression equation, round values to two decimal places, include the restricted.

00:30 Domain.

00:31 So this is, what i did was in excel, i made this scatter plot here and i was able to get the equation or the best fitting line.

00:48 And so for my equation, i would get y equals and then it wants you to round to two decimal places.

00:56 So 102 .92 plus.

01:01 Plus 1 .51 x.

01:07 Okay? and it says, interpret the slope from part b in the context of this problem.

01:13 Pay attention to the units.

01:15 Every time we increase by 1 .51, 1 .51.

01:28 So because i don't know what these say, i would say every time, every time we increase by 1 .51 centimeters of height, we increase by one centimeter for the metacarpal.

02:11 Okay.

02:12 So the predicted height for a random selected set of skeleton remains that has a length of the metacarpal of 41 centimeters is, so i would do y equals 102 .92 plus 1 .51 times 41...

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