To determine if the prediction of the number of owls in year 9 using the given quadratic regression model makes sense, we need to follow these steps:
1. Identify the Model: The quadratic regression equation given is [tex]\( y = -1.34x^2 + 10.75x - 11.3 \)[/tex].
2. Substitute Year into the Model: Substitute [tex]\( x = 9 \)[/tex] into the model to predict the number of owls in year 9.
[tex]\[
y = -1.34(9)^2 + 10.75(9) - 11.3
\][/tex]
3. Calculate the Predicted Number of Owls:
- First, calculate [tex]\( 9^2 \)[/tex]:
[tex]\[
9^2 = 81
\][/tex]
- Then, multiply by the coefficient of [tex]\( x^2 \)[/tex]:
[tex]\[
-1.34 \times 81 = -108.54
\][/tex]
- Next, multiply [tex]\( 10.75 \)[/tex] by [tex]\( 9 \)[/tex]:
[tex]\[
10.75 \times 9 = 96.75
\][/tex]
- Finally, add the results and subtract [tex]\( 11.3 \)[/tex]:
[tex]\[
y = -108.54 + 96.75 - 11.3
\][/tex]
[tex]\[
y = -23.09
\][/tex]
4. Interpret the Result: The predicted number of owls for year 9 is [tex]\( -23.09 \)[/tex].
5. Analyze the Prediction:
- A predicted result of [tex]\( -23.09 \)[/tex] owls is not realistic because a population cannot be negative.
- This indicates that the model's prediction for year 9 does not make sense.
6. Conclusion: Given that a negative number of owls is not possible in a realistic context, the prediction does not make sense. Therefore, the best choice among the provided options is:
C. No, because you can't have a negative number of owls.
