4. Using linear regression, develop a forecast for month 9 for the following data: Month Warehouse Space Requirements (square feet) 1 15,525 2 16,750 3 17,250 4 18,000 5 18,257 6 18,785 7 19,280 8 19,575 The sad truth about forecasts is that they are almost always wrong. It is very difficult to predict the future with precision. There are many events or scenarios that can change actual results. As the forecast horizon lengthens, confidence in the accuracy of the forecast diminishes because the historical patterns on which the forecast is based may not continue into the future. Two basic ways of measuring forecasting error are the mean squared error (MSE) and the mean absolute deviation (MAD). These two methods are discussed in greater detail in the following sections. Mean Squared Error The mean squared error (MSE) is the average of all the squared errors. To calculate the MSE, square the differences between each actual value and the forecasted value, add these squared values together, and then divide by the total number of observations. The following data, used in the exponential smoothing section of this supplement, can be used to illustrate this calculation. Actual Forecasted Squared Period Demand Demand Error Error 7 48 52.69 4.69 22.00 8 45 51.15 6.15 37.82 9 47 49.13 2.13 4.54 10 45 48.43 3.43 11.76 11 40 47.31 7.31 53.44 Total
129.56 The MSE of 25.91 resulted from forecasts obtained using an exponential smoothing constant of 0.328 in the previous exponential smoothing section. For comparison sake, let’s calculate the MSE of the forecasts obtained using an exponential smoothing constant of 0.793. Actual Forecasted Squared Period Demand Demand Error Error 7 48 52.69 4.69 22.00 8 45 48.97 3.97 15.76 9 47 45.82 1.18 1.39 10 45 46.76 1.76 3.10 11 40 45.36 5.36 28.73 Total
70.98 MSE 70.98 5

14.20