Question

Evaluating Extrapolated Predictions
A graph has average temperature (degrees Fahrenheit) on the x-axis, from 0 to 60, and total coat sales on the y-axis, from 0 to 100. A trend line goes through points (55, 50) and (65, 40). The regression equation is y = negative 0.96 x + 103.

What can be concluded about the extrapolated data for this scenario? Check all that apply.
The predictions will always be accurate.
Eventually the coat sales will be negative, which is not possible.
Eventually the temperature will increase or decrease to impossible values.
The coat sales will continue to increase as the temperature increases.
Some predictions may not be accurat

Answer 1

Select:
- Eventually the coat sales will be negative, which is not possible.
- Some predictions may not be accurate.

Reason: The slope is -0.96 so the model predicts fewer coats as temperature rises; extrapolating far enough (y = -0.96x + 103 gives y = 0 at x ≈ 107°F) yields negative sales, which is unrealistic. Also, linear models can be unreliable outside the range of the observed data, so extrapolated predictions may be inaccurate. The other statements are false.