Question

Using the data below, calculate the bias based on using the naïve forecast method. Week Time Series Value 1 9.00 2 14.00 3 24.00 4 20.00 Submit Answer format: Number: Round to: 1 decimal places. unanswered not_submitted Attempts Remaining: 5

Answer 1

The bias of the naïve forecast method, given the time series values, is calculated by averaging the forecast errors over the three weeks provided, resulting in a bias of 3.7 when rounded to one decimal place.

Step-by-step explanation:

To calculate the bias using the naïve forecast method, we examine the prediction errors made when we forecast the next period's value by simply using the last period's actual value. For the given data, we compare the actual values for weeks 2 to 4 with the forecasted values, which are the actual values from weeks 1 to 3.

• For week 2, the forecasted value would be that of week 1, which is 9, so the error is 14 - 9 = 5.
• For week 3, the forecasted value would be that of week 2, which is 14, so the error is 24 - 14 = 10.
• For week 4, the forecasted value would be that of week 3, which is 24, so the error is 20 - 24 = -4.

The bias is then the average of these errors: (5 + 10 - 4)/3 = 11/3 ≈ 3.7. Therefore, the bias is 3.7 when rounded to 1 decimal place.

Answer 2

To calculate the bias using the naïve forecast method, we compare the forecasted value with the actual value for available weeks. The bias for each week's forecast is 5.00 for Week 2, 10.00 for Week 3, and -4.00 for Week 4, summing up to a total bias of 11.00 over the three weeks.

Step-by-step explanation:

The student is asked to calculate the bias using the naïve forecast method based on the time series data. The naïve forecasting method assumes that the value of the time series at the next time period will be the same as its current value. To calculate the bias, we compare the forecasted value with the actual value and sum these differences over the period. In this example, the bias is based on the following weeks and corresponding values:

• Week 1: 9.00 (No forecast, since it's the first observation)
• Week 2: 14.00
• Week 3: 24.00
• Week 4: 20.00

The forecast for each week is the value of the previous week. Hence, the forecasts are:

• Week 2 forecast: 9.00
• Week 3 forecast: 14.00
• Week 4 forecast: 24.00

The bias is calculated by taking the sum of the differences between the actual values and the forecasted values:

• Bias (Week 2): 14.00 - 9.00 = 5.00
• Bias (Week 3): 24.00 - 14.00 = 10.00
• Bias (Week 4): 20.00 - 24.00 = -4.00

Sum of biases: 5.00 + 10.00 - 4.00 = 11.00

The total bias over the three weeks that had forecasts is 11.00. Since the question asks for positive or negative bias, this summed value represents the bias without an average. To express the bias as an average bias per period, we would divide the total bias by the number of periods with forecasts. In this case, there are 3 periods with forecasts (Week 2, 3, and 4), so the average bias would be 11.00 / 3 = 3.67, rounded to 1 decimal place as per instructions, which would be 3.7.