Answer :
Answer: First of all, we will add the options.
A. Yes, because 3 inches falls above the maximum value of lengths in the sample.
B. Yes, because the regression equation is based on a random sample.
C. Yes, because the association between length and weight is positive.
D. No, because 3 inches falls above the maximum value of lengths in the sample.
E. No, because there may not be any 3-inch fish of this species in the pond.
The correct option is D.
Step-by-step explanation: It would not be appropriate to use the model to predict the weight of species that is 3 inches long because 3 inches falls above the maximum value of lengths in the sample.
As we can see from the question, the model only accounts for species that are within the range of 0.75 to 1.35 inches in length, and species smaller or larger than that length have not been taken into consideration. Therefore the model can not be used to predict the weights of fishes not with the range accounted for.
Here, we are required to decide if it'd be appropriate to use the 0.75 to 1.35 inches model to predict the weight of a fish of this species that is 3 inches long.
- No, and this is because the model is only valid for predictor values for which the data has sufficient values and 3 inches falls out of range.
- A very important detail about regression models is that they can not be used to extrapolate beyond the range of data.
- However, in the situation above, the single linear regression model developed by the biologist is is valid only for lengths which vary between 0.75 to 1.35.
Therefore, a 3inches long specie of this fish would require extrapolation out of the model's range and as such, it is not appropriate.
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