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Dem bones Archaeopteryx is an extinct beast having feathers like a bird but teeth and a long bony tail like a reptile. Only six fossil specimens are known. Because these specimens differ greatly in size, some scientists think they are different species rather than individuals from the same species. We will examine some data. If the specimens belong to the same species and differ in size because some are younger than others, there should be a positive linear relationship between the lengths of a pair of bones from all individuals. An outlier from this relationship would suggest a different species. Here are data on the lengths in centimeters of the femur (a leg bone) and the humerus (a bone in the upper arm) for the five specimens that preserve both bones:$8$

(a) How would $r$change if the bones had been measured in millimeters instead of centimeters? (There are $10$millimeters in a centimeter.)

(b) If the $x$ and $y$ variables are reversed, how would the correlation change? Explain.

Step by step solution

01

Part (a) Step 1: Given Information

Data:

02

Part (a) Step 2: Explanation 

Because the linear correlation coefficient $r$is unit-independent, altering the units has no effect on the linear correlation coefficient.

03

Part (b) Step 1: Given Information 

Data:

04

Part (b) Step 2: Explanation

The linear correlation between the variables is unaffected by altering the variables, hence the linear correlation coefficient $r$remains intact.

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