Armspan and Height Leonardo da Vinci (1452–1519) drew a sketch of a man, indicating that a person’s armspan (measuring across the back with your arms outstretched to make a “T”) is roughly equal to the person’s height. To test this claim, we measured eight people with the following results:
Person | 1 | 2 | 3 | 4 |
Armspan (inches) | 68 | 62.25 | 65 | 69.5 |
Height (inches) | 69 | 62 | 65 | 70 |
Person | 5 | 6 | 7 | 8 |
Armspan (inches) | 68 | 69 | 62 | 60.25 |
Height (inches) | 67 | 67 | 63 | 62 |
a. Draw a scatterplot for armspan and height. Use the same scale on both the horizontal and vertical axes. Describe the relationship between the two variables.
b. If da Vinci is correct, and a person’s armspan is roughly the same as the person’s height, what should the slope of the regression line be?
c. Calculate the regression line for predicting height based on a person’s armspan. Does the value of the slope b confirm your conclusions in part b?
d. If a person has an armspan of 62 inches, what would you predict the person’s height to be?
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