Question

Suppose that the longevity (or life span) of mammals is something we have a good deal of information about and typically understand well, but the gestation period (or the length of pregnancy) of mammals is less clear. We therefore want to think about how we might be able to predict or explain gestation period based on longevity, especially if we uncover a new species of mammal. The scatterplot below shows the relationship between longevity (measured in years) and gestation (measured in days) for a sample of 38 mammals. The correlation between gestation and longevity is r = 0.59. The regression equation to predict gestation based on longevity is: Predicted gestation = 19.66 + 12.68 (longevity).

1. Would it be correct to say the units for r are “years per day”? Please explain why or why not.

2. An elephant has a longevity of 56 years. Should the regression equation be used to predict the elephant’s gestation period? Please explain why or why not.

3. A hedgehog has a longevity of 3 years. Should the regression equation be used to predict the hedgehog’s gestation period? Please explain why or why not.

4. Suppose you switched “x” and “y” in this example. In other words, rather than have x = longevity and y = gestation, you decide that x should be gestation and y should be longevity.

1. Would you expect the correlation coefficient, or r, to change if you switch “x” and “y”? Please explain.

2. Would you expect the regression equation to change if you switch “x” and “y”? Please explain.

Answer 1

1)

No because r is regression coefficient without any unit. A positive coefficient indicates that as the value of the independent variable increases, the mean of the dependent variable also tends to increase.

1. An elephant has a longevity of 56 years. Should the regression equation be used to predict the elephant’s gestation period? Please explain why or why not.

Depending on the data :

If the value 56 is outside the data points and then we are actually extrapolaring the data points to predict which is not correct. If it is within the data points then we are good.

1. A hedgehog has a longevity of 3 years. Should the regression equation be used to predict the hedgehog’s gestation period? Please explain why or why not.

Depending on the data :

If the value 3 is outside the data points and then we are actually extrapolaring the data points to predict which is not correct. If it is within the data points then we are good.

1. Would you expect the correlation coefficient, or r, to change if you switch “x” and “y”? Please explain.

NO, correlation coefficient does not depend on the order.

1. Would you expect the regression equation to change if you switch “x” and “y”? Please explain.

YES , equation became changed

Please let me know in case of any doubt.

Thanks in advance!

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