HW-forecasting NM

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Capella University *

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ACC3410

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Business

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Apr 3, 2024

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Homework Assignment – Forecasting Note : Submit both a Word document that includes the results and your reasoning, and an Excel file that contains necessary data analysis. 1. Bruce is a street vendor selling T-shirts in New York City. His sales in the past ten weeks are listed below. He wants to prepare for future sales in week 11 and 12. Weeks Sales 1 33 2 31 3 31 4 37 5 40 6 33 7 50 8 45 9 55 10 60 (a) (10 points) Bruce decides to first try the following time series methods: arithmetic mean (AM), last period value (LPV), moving average (MA) (3), MA (4), MA (5), exponential smoothing (ES) (0.1), ES (0.4), and ES (0.8). What are the forecasted sales in week 11 and 12 using these methods? Which is the best method, based on MFE, MAD and MSE? Based on the data entered in the excel we can see that for weeks 11 and 12 we are forecasting Week AM LPV MA (3) MA (4) MA (5) ES (0.1) ES (0.4) ES (0.8) 11 41.5 60 53.3 52.5 48.6 40.3 52.5 58.6 12 41.5 60 53.3 52.5 48.6 40.3 52.5 58.6 Now when we look at the error of the methods we get the below. Measure AM LPV MA (3) MA (4) MA (5) ES (0.1) ES (0.4) ES (0.8) MFE -7.82 -3.00 -7.00 -8.71 -10.08 -8.15 -5.43 -3.56 MAD 8.80 6.11 7.86 9.29 10.64 9.16 6.87 5.87 MSE 126.37 59.67 76.05 111.11 144.94 140.38 70.31 54.16 (b) (8 points) Bruce wants to further try out the simple linear regression. What is the regression model computed using Excel (Data Analysis add-in)? Is the

model valid according to the residual plot? What is the significance of the model ( R 2 and p -value of the slope)? When we look at the simple linear regression from the data we see that Y=3.109X+24.4, Y is the forecasted sales while x is the week number. The residual plot below shows that the residuals are random.The model obtained is a good model to use, because the p-value of the slope is 0.00047 (much smaller than 0.05), and R 2 is reasonably close to 1 (0.80). (c) (2 points) Comparing the regression method to the smoothing methods, which one should Bruce choose? Why? What will be the best forecast for sales in week 11 and 12 ? In order to compare the regression method to the smoothing methods, We will need to use the same error measures. We see that the MFE, MAD, and MSE have already been figured out, this shows we should be using the same error measures for the regression methods. When we run the regression model in Excel, we need to ensure that we are using the “residuals” option. We need to ensure that we are using the negative value for the residuals as well. When looking at excel we see that the MFE is 0.00, MAD is 3.41, and MSE is 19.90. All of the error measures show that the regression method is better then the best method in part a. With this Bruce should be using the regression model to improve his sales forecasting for weeks 11 and 12. Sales in week 11 = 3.109*11 + 24.40 = 58.60 Sales in week 12 = 3.109*12 + 24.40 = 61.71

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