Question

A biologist studying largemouth bass observed a quadratic relationship between the lengths and weights of fish in a large sample. The biologist took the base 101010 logarithm for the values of both variables, and they noticed a linear relationship in the transformed data.

Here's the least-squares regression equation for the transformed data, where weight is in kilograms and length is in centimeters.

\widehat{\log(\text{weight})}=3.19\log(\text{length})-5.13

log(weight)

​

=3.19log(length)−5.13log, left parenthesis, start text, w, e, i, g, h, t, end text, right parenthesis, with, \widehat, on top, equals, 3, point, 19, log, left parenthesis, start text, l, e, n, g, t, h, end text, right parenthesis, minus, 5, point, 13

According to this model, what is the predicted weight of a largemouth bass that is 60\,\text{cm}60cm60, start text, c, m, end text long?

You may round your answer to one decimal place.

Answer 1

The predicted weight of a largemouth bass that is 60 cm long is approximately 15.8 kilograms.

Step-by-step explanation:

The predicted weight of a largemouth bass that is 60 cm long can be found using the regression equation. According to the given equation, the predicted weight can be calculated by substituting the length value into the equation:

log(weight) = 3.19 * log(length) - 5.13

Substituting the length of 60 cm into the equation:

log(weight) = 3.19 * log(60) - 5.13

Using the given logarithmic value of 60 as 101.7782, we can calculate:

log(weight) = 3.19 * 101.7782 - 5.13

Rounding the result to one decimal place, the predicted weight of a largemouth bass that is 60 cm long is approximately 15.8 kilograms.