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Leonardo da Vinci (1452-1519) drew a sketch of a man, indicating that a persons armspan (measuring across the back with arms outstretched to make a T) is roughly equal to the persons height. To test this clalm, we measured eight people with the following results. Person Armspan (inches) 6862.25 65 70.5 69 69 62 60.25 Height (inches) 67 61 64 70 66 67 61 61 (a) Draw a scatterplot for armspan and height. Use the same scale on both the horizontal and vertical axes Height (in) Height (in)

Height Height (in) 75 (in) 75 70 70 65 65 60 60 Armspan 75 (in) Armspan 75 (in) 60 65 70 60 65 70 Height Height (in) 75 (in) 75 70 70 65 65 60 60 Armspan 75 (in) Armspan 75 (in) 60 65 70 60 65

Describe the relationship between the two variables. There Is a negatlve linear relatlonshlp between armspan and helght. There Is no relationshlp between armspan and helght There is a positive linear relationship between armspan and height. (b) Calculate the correlation coefficient relating armspan and height. (Round your answer to three decimal places.) (c) If you were to calculate the regresslon llne for predlcting helght based on a persons armspan, how would you estlmate the slope of this lIne? SInce DaVIncl suggested that a persons armspan is roughly equal to hls helght, the slope of the lIne should be negatlve Since DaVinci suggested that a persons armspan is roughly equal to his height, the slope of the line should be greater than 1. ● since Davlncl suggested that a persons armspan is roughly equal to his height, the slope of the line should be approximately equal to 0. ● Since DaVincl suggested that a persons armspan ls roughly equal to his height, the slope of the line should be approximately equal to 1. (d) Find the regression line relating armspan x to a persons height y. (Round all numerical values to three decimal places.) (e) If a person has an armspan of 62 inches, what would you predict the persons height to be? (Round your answer to two decimal places.) in

math   Statistics-And-Probability   
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Answer #1

(y-y) 5.6406 13.1406 0.3906 28.8906 1.8906 5.6406 13.1406 13.1406 81.8750 (x-x)(y-y 5.3438 12.6875 0.4688 25.5313 4.4688 7.7188 13.5938 19.9375 89.7500 S.No (AT) X-X 5.0625 12.2500 0.5625 22.5625 10.5625 10.5625 14.0625 30.2500 105.8750 61 64 70 2 62.25 70.5 69 69 4 6 60.25 526 65.7500 61 61 517 64.6250 Total Mean SSY sample size here 64.6250 65.7500 from above 2(x-X)- 105.8750 89.7500 slope- 0.8477 intercept- 8.8889 hence line equation: 8.889 0.848 x correlation coefficient rS(VsSy - 0.964

a)

for scatterplot: top left curve is right

there is a positive linear relationship

b)

correlation coefficient r=0.964

c)

..should be approximately equal to 1

d)

yhat=8.889+0.848x

e)

predicted value =0.889+0.848*62=53.47

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