c Management believes when the average weekly demand for beds will be more than

# C management believes when the average weekly demand

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c. Management believes when the average weekly demand for beds will be more than 400, the ER will collapse. When does this situation expected to occur with 90% confidence, based on the Holt's forecasting? Use the model you found in question 'b' above. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 200 220 240 260 280 300 320 340 360 380 400 f(x) = 3.47842401500938 x + 262.192307692308 Series Column C Linear (Column C) a. The equation appears in the graph below. Here are the calculations for the next 6 weeks: Week 41 Demand = 3.478*41+262.19 = 404.788 42 Demand = 3.478*42+262.20 = 408.266 43 Demand = 3.478*43+262.21 = 411.744 44 Demand = 3.478*44+262.22 = 415.222 45 Demand = 3.478*45+262.23 = 418.7 b. To compare performance we need to determine MSE of the two models. For the regression this value is readily available in the template. MSE(Regression) = 222.25. For the Holt's model we need to first optimize its parameters alpha and gamma. We use "Data Table" for alpha and gamma. After solving we get: alpha = .25. and gamme = .35 I used margins of 0.05. MSE(Holt's) = 59.67 The Holt's model performs much better. c. This situation might occur in 5 weeks. At this time the upper limit of the 95% prediction interval will exceed 400. Note that the Holt's actual forecast F(t+k) remains under 400 for more than 12 periods ahead but when adding the confidence level consideration, it becomes 4 week. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 200 250 300 350 400 450 Chart Title Column J Column K Column E Column B Holt's forecasts  Problem 20 from the text pg. 410 Year Expenses % 1 13.9 a. It appears that a negative trend is present. 2 12.2 3 10.5 4 10.4 5 11.5 6 10 7 8.5 b. The model parameters can be found from the graphical tool directly: The Expenses percent = -0.7*t + 13.8 c. F(t=8) = -0.7*8+13.8 d. F(t) = -.7*t + 13.8 = 5 t = (5 - 13.8)/(-.7) = 12.57143 years Additional Analysis Now let us run the Holt's model on this data, and answewr the same quaestions. We'll p and then complete the analysis with the template. Let us use alpha = .3 and gamma L2 = 12.2. T2 = 12.2-13.9 = -1.7 F3 = 12.2+(-1.7) = 10.5 L3= .3*10.5 + 0.7*10.5 = 10.5 T3 = .2*(10.5-12.2)+.8*(-1.7) = -1.7 F4 = 10.5 +(-1.7) = 8.8 L5 = .3*11.4 +.7*8.8 = 9.58 T5 = .2*(9.58-10.5)+.8*(-1.7) = -1.544 F6 = 9.58+(-1.544) = 8.306 c. As of period 7 we have (from the termplate) L7 = 7.444 T7 = -1.131 F8 = L7 + T7 = 6.313 d. F(t) = 7.444+(-1.131*t) = 5. Now solve for 't'. 1 2 3 4 5 6 7 5 7 9 11 13 15 f(x) = − 0.7 x + 13.8 Chart Title practice a few stages at the beginning = .2. Problem 21 from the textbook (pg. 411) Year Cost/Unit 1 20 2 24.5 3 28.2 4 27.5 5 26.6 6 30 7 31 8 36 a. The pattern exhibits positive linear trend b. The regression prediction equation is: Unit Cost = 1.7738t+19.993 c. The average cost increase is 1.7738 per year. d. The unit cost next year is expected to be F(9) = 1.7738(9) + 19.993 Additional analysis (i) You were offerred to use erxponential smoothing for the foreast of this time series.  #### You've reached the end of your free preview.

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