Question

In: Statistics and Probability

Does knee height predict overall height? Since elderly people may have difficulty standing to have their...

Does knee height predict overall height? Since elderly people may have difficulty standing to have their heights measured, a study looked at predicting overall height (y) in centimeters, from height to the knee (x) in centimeters. Use this data to answer the following questions.

Data looking at knee height (in cm) and overall height (in cm)

Knee

Height (cm)

57.70

47.40

43.50

44.80

55.20

54.60

Overall Height (cm)

192.10

153.30

146.40

162.70

169.10

177.80
  1. What is the mean x and standard deviation sxof x?
  2. What is the mean y and standard deviation sy of y?
  3. What is the correlation r of x and y? What does the correlation mean?
  4. The least-squares regression line. (3 pts)

  1. What is the value of the slope?
  2. What is the value of the intercept?
  3. What is the equation of the least-squares regression line

  1. Someone with a knee height of 65 cm would be approximately 220 cm tall. Is this a good use of the least-squares regression line? Why or why not? (2 pts)
  2. What is the mean x and standard deviation sxof x?
  3. What is the mean y and standard deviation sy of y?
  4. What is the correlation r of x and y? What does the correlation mean?
  5. The least-squares regression line. (3 pts)

    1. What is the value of the slope?
    2. What is the value of the intercept?
    3. What is the equation of the least-squares regression line?

  9. What is the coefficient of determination r2AND what does it tell you about the least-squares regression line? (2 pts)

  11. What is the predicted height for someone with a knee height of 430? (2 pts)

  13. Someone with a knee height of 65 cm would be approximately 220 cm tall. Is this a good use of the least-squares regression line? Why or why not? (2 pts)
  14. What is the mean x and standard deviation sxof x?
  15. What is the mean y and standard deviation sy of y?
  16. What is the correlation r of x and y? What does the correlation mean?
  17. The least-squares regression line. (3 pts)

    1. What is the value of the slope?
    2. What is the value of the intercept?
    3. What is the equation of the least-squares regression line?

  21. What is the coefficient of determination r2AND what does it tell you about the least-squares regression line? (2 pts)

  23. What is the predicted height for someone with a knee height of 430? (2 pts)

  25. Someone with a knee height of 65 cm would be approximately 220 cm tall. Is this a good use of the least-squares regression line? Why or why not? (2 pts)

Solutions

Expert Solution

Knee height (X) overall height (Y) XY X2 Y2
57.7 192.1 11084.17 3329.29 36902.41
47.4 153.3 7266.42 2246.76 23500.89
43.5 146.4 6368.4 1892.25 21432.96
44.8 162.7 7288.96 2007.04 26471.29
55.2 169.1 9334.32 3047.04 28594.81
54.6 177.8 9707.88 2981.16 31612.84
Total 303.2 1001.4 51050.15 15503.54 168515.2

n = 6

a)

The equation of the least-squares regression line is given by

where

The formula for finding slope is given by

Therefore,the value of the slope = 2.45

b)

The formula for finding intercept is given by

We have

Now

= 42.93

Therefore,the value of the intercept = 42.93

c)

The equation of the least-squares regression line is

When knee height (x) =  65 cm

= 42.93 + 2.45*65

= 202.18

Overall Height = 202.18 cm

Finding mean and standard deviation of X

Mean of X = 50.53

= 6.03

Finding mean and standard deviation of Y

Mean of Y = 166.9

Finding correlation r of x and y

The formula for finding correlation coefficient is given by

= 0.89

The correlation coefficient between x and y is 0.89

It indicates a strong uphill (positive) linear relationship.

Finding coefficient of determination (R2)

coefficient of determination is the square of the correlation coefficient.

coefficient of determination = R2 = 0.892 = 0.7921

R2  of  0.7921 suggests that 79.21% of the dependent variable is predicted by the independent variable.

When  knee height (X) = 430 cm

= 42.93 + 2.45*430

= 1096.43

Overall Height = 1096.43 cm

The predicted height for someone with a knee height of 430 cm is 1096.43 cm

orchestra answered 1 year ago
Next > < Previous

Related Solutions

Does knee height predict overall height? Since elderly people may have difficulty standing to have their...
Does knee height predict overall height? Since elderly people may have difficulty standing to have their heights measured, a study looked at predicting overall height (y) in centimeters, from height to the knee (x) in centimeters. Use this data to answer the following questions. Data looking at knee height (in cm) and overall height (in cm) Knee Height (cm) 57.70 47.40 43.50 44.80 55.20 54.60 Overall Height (cm) 192.10 153.30 146.40 162.70 169.10 177.80 What is the mean x and...
Because elderly people may have difficulty standing to have their height measured, a study looked at...
Because elderly people may have difficulty standing to have their height measured, a study looked at the relationship between overall height and height to the knee. Here are data (in centimeters) for five elderly men: Knee Height ? 56.5 46.3 41.2 47.7 52.7 Height ? 192.4 151.8 149.7 162.1 174.5 What is the equation of the least-squares regression line for predicting height from knee height? ANSWER: ?̂ =
Because elderly people may have difficulty standing to have their height measured, a study looked at...
Because elderly people may have difficulty standing to have their height measured, a study looked at the relationship between overall height and height to the knee. Here are data (in centimeters) for five elderly men: Knee Height x 57.2 45.7 42.9 45.6 52.4 Height y 191.6 153.7 145.2 163.6 174.3 What is the equation of the least-squares regression line for predicting height from knee height? ANSWER: ŷ =
1: A nurse may have difficulty implementing a middle-range theory that a. Does not support personal...
1: A nurse may have difficulty implementing a middle-range theory that a. Does not support personal experience b. Results in an intended outcome c. Has applicability in many different nursing environments d. All of the above 2: Middle-range theories are based on a. Research b. Personal experience c. Observation d. All of the above 3: To be considered a middle-range theory, what does a nursing theory require? a. Support from the academic nursing community b. Ties to pre-existing nursing theories...
Because some people are unable to stand to have their height measured, doctors use the height...
Because some people are unable to stand to have their height measured, doctors use the height from the floor to the knee to approximate their patients’ height (in cm). Height of Knee Overall Height 57.7 192.3 47.5 153.3 43.5 146.2 44.8 160.4 55.6 171.4 54.9 176.7 a. Use Excel to determine the correlation coefficient of this data b. Use Excel to determine the regression equation of this data c. Find the overall height from a knee height of 45.3 cm...
Because some people are unable to stand to have their height measured, doctors use the height...
Because some people are unable to stand to have their height measured, doctors use the height from the floor to the knee to approximate their patients’ height (in cm). Height of Knee Overall Height 57 192 47 153 43 146 44 160 55 171 54 176 a. Use Excel to determine the correlation coefficient of this data b. Use Excel to determine the regression equation of this data c. Find the overall height from a knee height of 45.3 cm...
A psychologist noted that people have more difficulty sleeping in a bright room than in a...
A psychologist noted that people have more difficulty sleeping in a bright room than in a dark room. She measured whether the intensity of the light could predict the time it took a sample of 4 participants to fall asleep. The data for this hypothetical study are listed in the following table. Intensity of Light (in watts) Time It Took to Sleep (in minutes) X Y 5 13 10 20 20 32 40 37 Compute an analysis of regression for...
A psychologist noted that people have more difficulty sleeping in a bright room than in a...
A psychologist noted that people have more difficulty sleeping in a bright room than in a dark room. She measured whether the intensity of the light could predict the time it took a sample of 4 participants to fall asleep. The data for this hypothetical study are listed in the following table. Intensity of Light (in watts) Time It Took to Sleep (in minutes) X Y 5 8 10 16 20 27 40 34 Compute an analysis of regression for...
A psychologist noted that people have more difficulty sleeping in a bright room than in a...
A psychologist noted that people have more difficulty sleeping in a bright room than in a dark room. She measured whether the intensity of the light could predict the time it took a sample of 4 participants to fall asleep. The data for this hypothetical study are listed in the following table. Intensity of Light (in watts) Time It Took to Sleep (in minutes) X Y 5 12 10 21 20 33 40 36 Compute an analysis of regression for...
A psychologist noted that people have more difficulty sleeping in a bright room than in a...
A psychologist noted that people have more difficulty sleeping in a bright room than in a dark room. She measured whether the intensity of the light could predict the time it took a sample of 4 participants to fall asleep. The data for this hypothetical study are listed in the following table. Intensity of Light (in watts) Time It Took to Sleep (in minutes) X Y 5 10 10 18 20 32 40 36 Compute an analysis of regression for...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT