Question

compare a predicted value to an actual value and calculate the percent error. you must: - state the predicted value and actual value - calculate the percent error - show all steps in your calculation - explain what the percent error tells you about the accuracy of the prediction

Explanation:

To solve this, we'll use an example. Let's say the predicted value is \( 50 \) and the actual value is \( 45 \).

Step 1: Identify predicted and actual values

Predicted value (\( V_{predicted} \)) = \( 50 \)
Actual value (\( V_{actual} \)) = \( 45 \)

Step 2: Calculate the absolute error

Absolute Error = \( |V_{predicted} - V_{actual}| \)
\( |50 - 45| = 5 \)

Step 3: Calculate percent error

Percent Error = \( \frac{\text{Absolute Error}}{|V_{actual}|} \times 100\% \)
\( \frac{5}{45} \times 100\% \approx 11.11\% \)

of Percent Error Interpretation:
Percent error measures the relative difference between the predicted and actual values. A smaller percent error (closer to 0%) means the prediction is more accurate. Here, a ~11.11% error suggests the prediction was moderately off from the actual value. If the percent error were 0%, the prediction would be perfectly accurate. Larger percent errors indicate greater inaccuracy in the prediction.

Answer:

• Predicted value: \( 50 \), Actual value: \( 45 \)
• Percent Error: \( \approx 11.11\% \)
• Interpretation: A ~11.11% percent error shows the prediction has a moderate deviation from the actual value; smaller percent error implies higher prediction accuracy.