Question

A marine biologist, a scientist who studies animals that live in the water, created an equation for the least squares regression line to predict the length of a great white shark based on the height of its dorsal fin. The height of the dorsal fin of one particular great white shark was 23 inches and the equation predicted a length of 13 feet. The prediction was not perfect. The residual for this fish was 0.8. Which of the following statements is true?

A)The great white shark was actually 12.2 feet long.
B) The great white shark was actually 13.0 feet long.
C)The great white shark was actually 13.8 feet long.
D)The dorsal fin was actually 22.2 inches long.

Answer 1

The correct statement is that the great white shark was actually 13.8 feet long, deduced by adding the residual to the predicted length.

Step-by-step explanation:

The student asked about a regression analysis in a marine biology context, looking to understand the relationship between the height of a great white shark's dorsal fin and its length. In this scenario, the residual is the difference between the observed value and the value predicted by the regression equation. Because the residual for the shark in question is 0.8 feet, and the predicted length is 13 feet, we add the residual to the predicted length to find the actual length: 13 feet + 0.8 feet, making the great white shark actually 13.8 feet long. Therefore, the correct statement is C) The great white shark was actually 13.8 feet long.