Question

8.4.3 test (cst): data and mathematical modeling
this table shows the population of owls in a park in different years. the quadratic regression equation that models these data is
$y=-1.34x^{2}+10.75x - 11.3$.
using this model, the predicted number of owls in year 8 is about - 11. does this prediction make sense? why or why not?

Explanation:

Step1: Analyze the nature of the variable

The variable \(y\) represents the number of owls. The number of owls cannot be negative in a real - world context.

Step2: Evaluate the prediction

Since the predicted value \(y=-11\) (where \(y\) is the number of owls) is negative, and the number of owls must be a non - negative quantity (you can't have a negative number of living organisms in this context).

Answer:

No, the prediction does not make sense. Because the number of owls (\(y\)) cannot be negative in reality, and the model predicts \(y = - 11\) for year \(8\).