Aplank rests on top of the axles of two identical wheels. each wheel's outer radius is $0.25 \; \mathrm{m},$ and each wheel's axle has radius $0.05 \; \mathrm{m}.$ if the wheels roll $1.00 \; \mathrm{m}$ from their original position, how much does the plank move from its original position? assume that there is no slipping anywhere, and that the plank does not tip.

1. We have:

MAE = 3.60

MSE = 15.60

MAPE = 25.45

2. We have:

MAE = 2.62

MSE = 11.11

MAPE = 19.59

3. The average of all the historical data provides the more accurate forecasts for the historical data.

Explanation:

Note: This question is not correct as the average of all the historical data is asked to be used as a forecast for the next period in requirements 1 and 2 instead of the naïve method (most recent value) for the first requirement. The correct question is therefore presented before answering the question as follows:

Consider the following time series data.

Week     1      2       3      4       5       6

Value    19    13      15     12     17      15

1. Using the naïve method (most recent value) as the forecast for the next period, compute the following (Round your answers to two decimal places.) measures of forecast accuracy:

a. Mean absolute error (MAE)

b. Mean squared error (MSE)

c. Mean absolute percentage error (MAPE).

2. Using the average of all the historical data as a forecast for the next period, compute the same three values. Round your answers to two decimal places.

3. Which method appears to provide the more accurate forecasts for the historical data?

The explanation of the answer is now provided as follows:

The following formulae are to be used:

MAE = Total of Error / Number of observations

MSE = Total of Error^2 / Number of observations

MAPE = Total of Error % / Number of observations

1. Using the naïve method (most recent value) as the forecast for the next period, compute the following (Round your answers to two decimal places.) measures of forecast accuracy:

Note: See part 1 of the attached excel file for the determination of Naïve and Calculations of Error, Error^2 and Error % using the naïve method as the forecast for the next period.

From the attached excel file, we have:

MAE = 18.00 / 5 = 3.60

MSE = 78.00 / 5 = 15.60

MAPE = 127.23 / 5 = 25.45

2. Using the average of all the historical data as a forecast for the next period, compute the same three values. Round your answers to two decimal places.

Note: See part 2 of the attached excel file for the determination of Naïve and Calculations of Error, Error^2 and Error % using the average of all the historical data as a forecast for the next period.

From the attached excel file, we have:

MAE = 13.12 / 5 = 2.62

MSE = 55.55 / 5 = 11.11

MAPE = 97.94 / 5 = 19.59

3. Which method appears to provide the more accurate forecasts for the historical data?

The average of all the historical data provides the more accurate forecasts for the historical data comparing the values of its MAE, MSE and MAPE to the values of MAE, MSE and MAPE of Naive method. This is because the error values of the average of all the historical data are much lowest and more closest to the actual data.