Question

the lengths and corresponding weights for 15 different - sized bluegill fish were measured and recorded. a regression analysis was completed and the computer output is given.
regression analysis: in(weight) versus in(length)
predictor coef se coef t p
constant - 5.28 0.54 - 9.777 0.000
in(length) 3.44 0.036 95.113 0.000
s = 0.0443 r - sq = 0.99 r - sq(adj) = 0.995
what is the equation of the least - squares regression line?
weight = 3.44 - 5.28 in(length)
length = - 5.28 + 3.44 in(weight)
in(weight) = 3.44 - 5.28 in(length)
in(weight) = - 5.28 + 3.44 in(length)

Explanation:

Step1: Recall the form of the least - squares regression line for a transformed model

The general form of a regression line for a model with transformed variables \(y\) and \(x\) (here \(y = \ln(\text{Weight})\) and \(x=\ln(\text{Length})\)) is \(\hat{y}=b_0 + b_1x\), where \(b_0\) is the intercept and \(b_1\) is the slope.

Step2: Identify the intercept and slope from the regression output

From the regression analysis table, the coefficient of the constant (\(b_0\)) is \(- 5.28\) and the coefficient of \(\ln(\text{Length})\) (\(b_1\)) is \(3.44\).

Step3: Substitute into the regression line formula

Substituting \(y = \ln(\text{Weight})\) and \(x=\ln(\text{Length})\) into \(\hat{y}=b_0 + b_1x\), we get \(\ln(\widehat{\text{Weight}})=-5.28 + 3.44\ln(\text{Length})\)

Answer:

\(\ln(\widehat{\text{Weight}})=-5.28 + 3.44\ln(\text{Length})\) (the fourth option)