The scatterplot shows data on the number of visitors to a resort each week since opening. A regression function is graphed with r^2=0.99. The predicted number of visitors after 16.4weeks is 38.6.
Is this prediction appropriate?
A.
No. The r^2value indicates a strong fit, but x=16.4is more than 50%of the range beyond the maximum value.
B.
No. The r^2value indicates a moderate fit, but x=16.4is more than 25%of the range beyond the maximum value.
C.
Yes. The r^2value indicates a strong fit, and x=16.4is within 50%of the range of the maximum value.
D.
Yes. The r^2value indicates a moderate fit, and x=16.4is within 25%of the range of the maximum value.
This means the model is a very strong fit for the data because 0.99is close to 1.
However, a strong r^2value does not automatically make every prediction appropriate. We also have to check whether the x-value is within a reasonable extrapolation range.
The data shown on the graph appear to extend to about:
x=11
The prediction is for:
x=16.4
This is far beyond the observed data range. Even though the model fits the known data very well, predicting too far beyond the data can be unreliable.
The correct statement is that the r^2value indicates a strong fit, but x=16.4is more than 50%of the range beyond the maximum observed value.
Therefore, the correct answer is:
▭ ( " A " )
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