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

C management believes when the average weekly demand

This preview shows page 5 - 11 out of 33 pages.

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)
Image of page 5
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
Image of page 6
Image of page 7
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
Image of page 8
practice a few stages at the beginning = .2.
Image of page 9
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.
Image of page 10
Image of page 11

You've reached the end of your free preview.

Want to read all 33 pages?

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture