A Biology student who created a regression model to use a bird\'s Height when pe

Question

A Biology student who created a regression model to use a bird's Height when perched for predicting its Wingspan made the following two statements. Assuming the calculations were done correctly, explain what is wrong with each a) My R^2 of 93% shows that this linear model is appropriate. b) A bird 10 inches tall will have a wingspan of 17 inches. a) What is wrong with the statement My R^2 of 93% shows that this linear model is appropriate"? A The value of R^2 represents the probability that a data point does not fit the linear model, a large R^2 means that most points don't fit the model and the model is not appropriate. The value of R^2 does not tell whether the model is appropriate, but measures the strength of the linear relationship. A large R^2 could also be due to an outlier. A value of 93% is not a large enough value of R^2 to ensure that the linear model is appropriate. The required value for R^2 is 95%. There is nothing wrong with the statement, an R^2 value of 93% shows that this linear model is appropriate. b) What is wrong with the statement "A bird 10 inches tall will have a wingspan of 17 inches A. This linear model is meant to predict Height using wingspan, and appropriate statement would be "A bird with a wingspan of 17 inches will have a height of 10 inches B. The variables Height and Wingspan should not be using the same units (inches). c. Predictions based on a regression line are for average values of y for a given x. The actual wingspan will vary around the prediction. D. There is nothing wrong with the statement, assuming all calculations are correct, a bird 10 inches tall will have a wingspan of 17 inches. Click to select your answer.

Explanation / Answer

1) What is wrong with the statement "My R2 of 93% shows that this linear mode is appropriate"?

ANSWER:

B. R2 does not tell whether the model is appropriate, but measures the strength of the linear relationship. High R2 could also be due to an outlier.

2)What is wrong with the statement "A bird 10 inches tall will have a wingspan of 17 inches"

ANSWER:

C. Predictions based on a regression line are for average values of y for a given x. The actual wingspan will vary around the prediction.

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