Question

1. for a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight based on its length. the biologist collects a random sample of this species of fish and finds that the lengths vary from 1.35 inches. the biologist uses the data from the sample to create a single linear regression model. would it be appropriate to use this model to predict the weight of a fish of this species that is 3 inches long? (a) yes, because 3 inches falls above the maximum value of lengths in the sample. (b) yes, because the regression equation is based on a random sample. (c) yes, because the association between length and weight is positive. (d) no, because 3 inches falls above the maximum value of lengths in the sample. (e) no, because there may not be any 3 - inch fish of this species in the pond. a set of bivariate data was used to create a least - squares regression line. which of the following is minimize

Explanation:

Step1: Understand Extrapolation

Extrapolation is using a regression model to predict values outside the range of the original data. Here, the sample lengths vary up to 1.35 inches (wait, maybe a typo? Wait, the problem says "lengths vary from... 1.35 inches"? Wait, no, maybe "up to 1.35 inches"? Wait, the question is about a 3 - inch fish. So the sample lengths are less than 3 inches (since 3 is above the sample's length range).

Step2: Evaluate Each Option

• Option A: Says yes because 3 is above max length, but extrapolation is risky. So A is wrong.
• Option B: Says yes because regression is based on random sample, but random sample doesn't justify extrapolation. Wrong.
• Option C: Says yes because positive association, but positive association doesn't justify extrapolation. Wrong.
• Option D: Says no because 3 inches is above the maximum length in the sample. Extrapolating beyond the data range is inappropriate for prediction, so this is correct.
• Option E: Says no because there may be no 3 - inch fish, but the issue is about using the model, not existence. So D is better.

Answer:

D. No, because 3 inches falls above the maximum value of lengths in the sample.