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.

Question

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 accurate.

Answer 1

In this scenario, let's analyze the conclusions based on the information provided about the graph and the regression equation \( y = -0.96x + 103 \).

1. The predictions will always be accurate.

   • False: Predictions made by extrapolating a linear regression can be subject to error, especially if they fall outside the range of the data used for the regression.

2. Eventually the coat sales will be negative, which is not possible.

   • True: As the temperature increases indefinitely, the regression equation indicates that coat sales (y) will approach negative values, which are not feasible in a real-world context.

3. Eventually the temperature will increase or decrease to impossible values.

   • True: Extrapolating beyond the average temperature range (0 to 60 degrees Fahrenheit) could suggest temperatures that are unrealistic (e.g., negative absolute temperatures or extreme values beyond typical weather).

4. The coat sales will continue to increase as the temperature increases.

   • False: The regression equation indicates that coat sales actually decrease as temperature increases.

5. Some predictions may not be accurate.

   • True: Since predictions based on extrapolation can lead to values outside the data's realistic range, some predictions made by this regression model may not be accurate.

In summary, the valid conclusions from the given options are:

• Eventually the coat sales will be negative, which is not possible.
• Eventually the temperature will increase or decrease to impossible values.
• Some predictions may not be accurate.