Question

the lengths, in inches, and corresponding weights, in ounces, for 15 different - sized bluegill fish were measured and recorded. given the regression equation, $ln(widehat{\text{weight}})=-5.28 + 3.44ln(\text{length})$, what is the expected weight for a bluegill fish that is 11 inches long?
19.47 ounces
31.19 ounces
32.56 ounces
37.84 ounces

Explanation:

Step1: Substitute length value

Substitute \( \text{Length} = 11 \) into the regression equation \( \ln(\text{Weight})=-5.28 + 3.44\ln(\text{Length}) \).
First, calculate \( \ln(11)\approx2.3979 \).
Then \( \ln(\text{Weight})=-5.28+3.44\times2.3979 \).

Step2: Calculate \( \ln(\text{Weight}) \)

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Step3: Solve for Weight

Since \( \ln(\text{Weight}) = 2.9787 \), then \( \text{Weight}=e^{2.9787} \).
Using a calculator, \( e^{2.9787}\approx 19.47 \).

Answer:

19.47 ounces