A fisherman has collected the following data about the length in inches, L, and weight in ounces, w of fish he has caught. The resulting line of best fit for the data is w=−37.1+3.2L

Question

Would predicting the weight of a 26-inch fish be interpolation or extrapolation? Explain.

(1 point)
Responses

Using the model to predict the weight of a 26-inch fish is interpolation because 26 inches is inside the range of the lengths in the data.
Using the model to predict the weight of a 26-inch fish is interpolation because 26 inches is inside the range of the lengths in the data.

Using the model to predict the weight of a 26-inch fish is extrapolation because 26 inches is inside the range of the lengths in the data.
Using the model to predict the weight of a 26-inch fish is extrapolation because 26 inches is inside the range of the lengths in the data.

Using the model to predict the weight of a 26-inch fish is extrapolation because 26 inches is outside the range of the lengths in the data.
Using the model to predict the weight of a 26-inch fish is extrapolation because 26 inches is outside the range of the lengths in the data.

Using the model to predict the weight of a 26-inch fish is interpolation because 26 inches is outside the range of the lengths in the data.
Using the model to predict the weight of a 26-inch fish is interpolation because 26 inches is outside the range of the lengths in the data.

Answer 1

Using the model to predict the weight of a 26-inch fish is interpolation because 26 inches is inside the range of the lengths in the data. Interpolation involves making predictions within the range of the data collected, while extrapolation involves making predictions outside of that range. Since the fisherman has data on lengths of fish he has actually caught, predicting the weight of a 26-inch fish falls within the range of the data and is therefore interpolation.