Question

0. A researcher examined a sample of rainbow trout taken from the Spokane River in Washington State, recording their lengths (mm) and weights (grams). For example, one trout was 360 mm long and weighed 469 g. Because a scatterplot using length to predic weight showed an exponential relationship, the researcher took the log of weight and successfully linearized the relationship. Use his regression model log(weight) = 1.491 +0.00331length to predict the weight of a 400 mm rainbow trout.

2.815 g
16.7 g
509 g
598 g
653 g​

Answer 1

To predict the weight of a 400 mm rainbow trout, the length is substituted into the regression model and the result is exponentiated. The weight of the trout is found to be approximately 653 grams.

Step-by-step explanation:

To predict the weight of a 400 mm rainbow trout using the regression model log(weight) = 1.491 + 0.00331length, we first substitute the given length into the equation:

log(weight) = 1.491 + 0.00331(400)

To find the weight itself, we need to take the antilogarithm (base 10) of the result to reverse the logarithmic transformation:

weight = 10^(1.491 + 0.00331(400))

Performing the calculations:

log(weight) = 1.491 + 1.324 = 2.815

weight = 10^2.815

Now, using a calculator to find the antilog, the predicted weight of the trout comes out to:

weight ≈ 653 g

Therefore, among the options provided, the predicted weight of a 400 mm rainbow trout is approximately 653 g, which is the correct option.