Archaeopteryx is an extinct animal having feathers like a bird but teeth and a long bony tail like a reptile. Only a few fossil specimens are known from the Jurassic geological period. If specimens belong to the same species then it is thought that there should be a strong relationship between the lengths of a pair of bones from all individuals. Data below is the length of the femur (a leg bone) and the humerus (an arm bone) for five specimens of Archaeopteryx fossil that have both bones. Femur length/cm | Humerus length/cm 38 | 37 52 | 62 59 | 63 64 | 75 74 | 84 a) Plot this data appropriately to decide if the length of the humerus bone can be predicted from the length of the femur. Present your graph well here. b) Is there a valid linear relationship? Show an appropriate plot as evidence for any statement. c) State the correlation value squared and state what this indicates.
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First, we need to plot the data points. The data given is: Humerus Length (x): 38, 52, 74 Femur Length (y): 37, 59, 84 Show moreā¦
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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: (a) Make a scatterplot. Do you think that all five specimens come from the same species? Explain. (b) Find the correlation $r$ step-by-step. First, find the mean and standard deviation of each variable. Then find the six standardized values for each variable. Finally, use the formula for $r$ . Explain how your value for $r$ matches vour graph in (a).
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Classifying Fossils. 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 belong to different 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. (a) Create an appropriately scaled and labeled scatter plot for these data. Would you say there is a strong or weak association or correlation? Is the association positive or negative? Justify your answers. (b) Find the correlation coefficient for these data. Does this correlation coefficient support your conclusions in part (a)? Why or why not? (c) Find the equation for the linear regression (best-fit line) for this data. Use it to predict the length of the humerus bone in Specimen 6 that did not preserve the humerus. The length of that femur bone is 44 centimeters.
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