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.

Explanation:

Step1: Analyze the linear model \( y = -0.96x + 103 \)

The equation represents the relationship between average temperature (\( x \)) and total coat sales (\( y \)). The slope is negative (\( -0.96 \)), so as \( x \) (temperature) increases, \( y \) (coat sales) decreases.

Step2: Evaluate "Predictions always accurate"

Extrapolation beyond the data range is uncertain. Real - world constraints (like non - negative sales) mean predictions can't always be accurate. So this statement is false.

Step3: Evaluate "Coat sales negative (impossible)"

Set \( y = 0 \), solve \( 0=-0.96x + 103\), \( x=\frac{103}{0.96}\approx107.29 \). For \( x>\frac{103}{0.96}\), \( y<0 \), but sales can't be negative. So this statement is true.

Step4: Evaluate "Temperature to impossible values"

The temperature range in real - world for this context (coat sales) is reasonable, and the model is about sales vs temperature, not temperature going to impossible values. So this statement is false.

Step5: Evaluate "Coat sales increase with temperature"

The slope is negative, so as temperature (\( x \)) increases, coat sales (\( y \)) decrease. So this statement is false.

Step6: Evaluate "Some predictions not accurate"

Due to real - world limits (e.g., non - negative sales) and extrapolation beyond data, some predictions may be inaccurate. So this statement is true.

Answer:

The correct statements are:

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