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The height of 10 skeletons (denoted by the variable stature) and the length of the middle metacarpal bone were measured (the metacarpal bones are in the hand between the wrist and fingers). The skeletal height is measured in centimeters and the metacarpal length in millimeters. The scatterplot is given below. 1. Describe what the scatterplot tells you about the direction, form, and strength of the relationship. stature (cm) 180.0 172.5 165.0 157.5+. O 39 45 51 metacarpal size (mm) 2. In this setting, is there a definite explanatory variable and response variable? Justify your answer. 3. Estimate the correlation between metacarpal length and stature. No calculations are necessary. 4. If the height and metacarpal length of the skeletons had been measured in inches, instead of centimeters and millimeters, how would the correlation between stature and metacarpal length for these 10 skeletons have been affected? Explain. 5. One of these skeletons (identified by the X) had a metacarpal size of 52 mm and a height of 183 cm. If the height of this skeleton had been incorrectly recorded as 153 cm, how would the correlation between stature and metacarpal length for these 10 skeletons change?

The height of 10 skeletons (denoted by the variable stature) and the length of the middle metacarpal bone were measured (the metacarpal bones are in the hand between the wrist and fingers). The skeletal height is measured in centimeters and the metacarpal length in millimeters. The scatterplot is given below. 1. Describe what the scatterplot tells you about the direction, form, and strength of the relationship. stature (cm) 180.0 172.5 165.0 157.5+. O 39 45 51 metacarpal size (mm) 2. In this setting, is there a definite explanatory variable and response variable? Justify your answer. 3. Estimate the correlation between metacarpal length and stature. No calculations are necessary. 4. If the height and metacarpal length of the skeletons had been measured in inches, instead of centimeters and millimeters, how would the correlation between stature and metacarpal length for these 10 skeletons have been affected? Explain. 5. One of these skeletons (identified by the X) had a metacarpal size of 52 mm and a height of 183 cm. If the height of this skeleton had been incorrectly recorded as 153 cm, how would the correlation between stature and metacarpal length for these 10 skeletons change?

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.8: Joint And Combined Variation
Problem 11P
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The height of 10 skeletons (denoted by the variable stature) and the length of the middle metacarpal bone were measured (the metacarpal bones are in the hand between the wrist and fingers). The skeletal height is measured in centimeters and the metacarpal length in millimeters. The scatterplot is given below. X 1. Describe what the scatterplot tells you about the direction, form, and strength of the relationship. stature (cm) 180.0 172.5 165.0 157.5 - . + + 51 39 45 metacarpal size (mm) 2. In this setting, is there a definite explanatory variable and response variable? Justify your answer. 3. Estimate the correlation between metacarpal length and stature. No calculations are necessary. 4. If the height and metacarpal length of the skeletons had been measured in inches, instead of centimeters and millimeters, how would the correlation between stature and metacarpal length for these 10 skeletons have been affected? Explain. 5. One of these skeletons (identified by the X) had a metacarpal size of 52 mm and a height of 183 cm. If the height of this skeleton had been incorrectly recorded as 153 cm, how would the correlation between stature and metacarpal length for these 10 skeletons change?
Transcribed Image Text:The height of 10 skeletons (denoted by the variable stature) and the length of the middle metacarpal bone were measured (the metacarpal bones are in the hand between the wrist and fingers). The skeletal height is measured in centimeters and the metacarpal length in millimeters. The scatterplot is given below. X 1. Describe what the scatterplot tells you about the direction, form, and strength of the relationship. stature (cm) 180.0 172.5 165.0 157.5 - . + + 51 39 45 metacarpal size (mm) 2. In this setting, is there a definite explanatory variable and response variable? Justify your answer. 3. Estimate the correlation between metacarpal length and stature. No calculations are necessary. 4. If the height and metacarpal length of the skeletons had been measured in inches, instead of centimeters and millimeters, how would the correlation between stature and metacarpal length for these 10 skeletons have been affected? Explain. 5. One of these skeletons (identified by the X) had a metacarpal size of 52 mm and a height of 183 cm. If the height of this skeleton had been incorrectly recorded as 153 cm, how would the correlation between stature and metacarpal length for these 10 skeletons change?
1. State Park rangers are interested in estimating the weight of the bears that inhabit their park. One way to estimate the weight of a bear is by measuring its neck girth (distance around the neck). One method used to accomplish this is to measure the bear's neck while it is hibernating, which is how some college students in Maine who were studying to be rangers and conservation officers got their data. 1. Sketch a well-labeled scatterplot Neck Girth Weight (pounds) (inches) 15 20.5 16 28 32 31 26.5 20 18 24 65 142 80 344 432 416 262 204 144 207 2. Describe what the scatterplot tells you about the direction and form of the relationship. 3. Using your calculator, find the value of the correlation. 4. Explain in words what this r says. 5. Use the scatterplot to predict the approximate weight of a bear with a neck girth of 22 inches. 6. Add a point to the scatterplot that would reduce the correlation between these variables. Explain why the point you added would have this effect.
Transcribed Image Text:1. State Park rangers are interested in estimating the weight of the bears that inhabit their park. One way to estimate the weight of a bear is by measuring its neck girth (distance around the neck). One method used to accomplish this is to measure the bear's neck while it is hibernating, which is how some college students in Maine who were studying to be rangers and conservation officers got their data. 1. Sketch a well-labeled scatterplot Neck Girth Weight (pounds) (inches) 15 20.5 16 28 32 31 26.5 20 18 24 65 142 80 344 432 416 262 204 144 207 2. Describe what the scatterplot tells you about the direction and form of the relationship. 3. Using your calculator, find the value of the correlation. 4. Explain in words what this r says. 5. Use the scatterplot to predict the approximate weight of a bear with a neck girth of 22 inches. 6. Add a point to the scatterplot that would reduce the correlation between these variables. Explain why the point you added would have this effect.
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