Question

evaluating extrapolated predictions
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:

• The first option is incorrect because extrapolated data is not always accurate.
• For the second option, if we consider the linear equation \(y = - 0.96x+103\), when \(y<0\), \(-0.96x + 103<0\), \(x>\frac{103}{0.96}\approx107.29\). Since \(y\) represents coat sales, negative sales are impossible.
• The third option is incorrect as the model is about coat sales (\(y\)) and temperature (\(x\)), not about temperature reaching impossible values.
• The fourth option is incorrect because the slope of the line \(y=-0.96x + 103\) is negative (\(m=-0.96\)), so as \(x\) (temperature) increases, \(y\) (coat sales) decreases.
• The fifth option is correct because extrapolation beyond the range of the original data can lead to inaccuracies.

Answer:

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