Consulting income at Kaplan Associates for the period February - July is shown in the table below. Assume that the initial forecast for February is $65,000. Use Exponential smoothing to forecast August's income.
Month Income ($1,000)
February 70.0
March 68.5
April 64.8
May 71.7
June 71.3
July 72.8
1. Use a smoothing constant of a = 0.2.
2. Use a smoothing constant of a = 0.5.
3. Which forecasting constant is best in this situation?0.2
Month Inc Forecast Trend FIT
Feb 70.0 65.0 0 65+0 = 65
Mar 68.5 0.1(70)+0.9(65) = 65.5 0.2(65.5-65)+(0.8)0 = 0.1 65.5+0.1=65.6
Apr 64.8 0.1(68.5)+0.9(65.6) = 65.89 0.2(65.89-65.5)+(0.8)0.1 = 0.16 65.89+0.16=66.05
May 71.7 0.1(64.8)+0.9(66.05) = 65.93 0.2(65.92-65.89)+(0.8)0.16 = 0.13 65.93+0.13=66.06
Jun 71.3 0.1(71.7)+0.9(66.06) = 66.62 0.2(66.62-65.93)+(0.8)0.13 = 0.25 66.62+0.25=66.87
Jul 72.8 0.1(71.3)+0.9(66.87) = 67.31 0.2(67.31-66.62)+(0.8)0.25 = 0.33 67.31+0.33=67.64
Aug 0.1(72.8)+0.9(67.64) = 68.16 0.2(68.16-67.31)+(0.8)0.33 = 0.43 68.16+0.43=68.60
Alpha 0.2
Error analysis Tracking Signal
Period Demand Forecast Error Absolute Squared Abs Pct Err Cum error Cum Abs Err Mad Track Signal (Cum error/MAD)
period 1 70 65 5 5 25 07.14% 5 5 5 1
Period 2 68.5 66 2.5 2.5 6.25 03.65% 7.5 7.5 3.75 2
Period 3 64.8 66.5 -1.7 1.7 2.89 02.62% 5.8 9.2 3.066666667 1.891304348
Period 4 71.7 66.16 5.54 5.54 30.6916 07.73% 11.34 14.74 3.685 3.07734057
Period 5 71.3 67.268 4.032 4.032 16.257024 05.65% 15.372 18.772 3.7544 4.094395909
Period 6 72.8 68.0744 4.7256 4.7256 22.33129536 06.49% 20.0976 23.4976 3.916266667 5.131826229
Total 20.0976 23.4976 103.4199194 33.29%
Average 3.3496 3.916266667 17.23665323 05.55%
Next period 69.01952 Bias MAD MSE MAPE
SE 5.084779232
6. Johnson Construction Company is in the process of installing power lines to a large housing development. The company wants to minimize the total length of wire used, which would minimize the company's cost. The housing development is shown below. Each house has been numbered, and the distances between houses are given in hundreds of feet.
1. What do you recommend to Johnson Construction Company?
7. The storm drains in the Cedar Rapids, Iowa, have been upgraded following the devastating floods of 2008. The network of storm drains and the capacities are shown below. Determine the maximum flow (in hundreds of gallons of water per minute) from node 1 to node 5. Remember that the arc has both capacity and reverse capacity.
From Node To Node Fluid Flow
1 2 250
2 1 100
1 3 100
3 1 150
1 4 400
4 1 400
1 5 150
5 1 200
2 4 300
4 2 200
3 4 250
4 3 300
3 5 300
5 3 250
4 5 300
5 4 0
8. From the States Data Set the following output for the Income in 2000 and for the Income in 2010 was created.
1. Which variable has the greatest relative variation?
9. You are a consultant working for Kaplan Consulting. The U.S. Department of Labor has requested assistance in evaluating the impact of economic stimulus on the unemployment rate. From the States Data Set the following t test was conducted to answer the question:
"Has there been a significant reduction in the national unemployment rate between January and June?"
1. What is the Null and the Alternative Hypotheses?
2. What is your level of alpha (a)?
3. What is your conclusion?
4. What is your answer to the question?
10. The Governor of a southern state has asked Kaplan Consulting to determine if the state were able to increase the percentage of its population with a Bachelor's Degree to 50%, what might be the expected median household income based on 2010 data? Here is the output from the Regression procedure from Excel.
1. What would be the predicted median household income if the percentage of the population in the state were