Quantitative Methods Quiz #2

Forecasting & Regression Analysis

3 MA Error 3 WMA Error

1. SalesForecast[Sales – Forecast]Forecast[Sales – Forecast]

Jan 64 -- --

Feb 70 -- --

Mar 68 -- --

Apr 64 67.333.33 68.204.20

May 72 67.333.33 65.806.20

Jun 71 68.003.00 69.201.80

July ? 69.00 70.60

Calculate the 3 month Moving Average for July, the 3 month Weighted Moving Average for July using weights of .60, .30, .10. Then use the date to estimate the MAD for each. Explain which is a better forecasting model?

3 MAMAD = (3.33+3.33+3.00)/3 = 3.22

3 WMAMAD = (4.20+6.20+1.80)/3 = 4.67

From the results of the MAD test we can see that the 3 MA model is a more accurate model for forecasting sales. The 3 MA had a MAD of 3.22 while the 3 WMA had a MAD of 4.67. Since the 3 MA is lower, it is more accurate.

2. n = 10 X = 55 Y = 207 X = 385 XY = 1228

  1. Use the above data to calculate the regression line Y = a + bX.
  2. If X = 12, what is the estimate for Y?
  3. If the Coefficient of Determination is 0.935 , explain what this means.

1228 – 10(5.5)(207)89.5

A. b = ------= 1.085

385 – 10(5.5) 82.5

a = 20.7 – 1.085(5.5) = 15.02Y = 15.02 + 1.085 X

B.Y = 15.02 + 1.085 (12) = 28.04

C. The Coefficient of Determination tells me the reliability of the regression line. Since it is 0.935, this means the resulting forecast is very reliable.

3. SalesForecast[Sales – Forecast]alpha x [Sales – Forecast]

Sept 41

Oct 42 411.000.40

Nov37 42.40 -5.40 -1.16

Dec33 35.84 -2.84 -1.14

Jan ? 31.86

Using an alpha constant = .40 , use Exponential Smoothing to Forecast sales for January.

4.Y = $90.00 + $48.50 X + $0.40 X Coefficient of Correlation = 0.68

Y = travel cost X = days on the road X = distance in miles traveled

A If Zhou Shan was on a business trip for 5 days and traveled 300 miles, what is the expected travel cost?

  1. Zhou submitted a request for reimbursement for $600, should it be paid? Why or Why not? Is this a valid model?
  1. Y = 90.00 + 48.50(5) + 0.40(300)

Y = 452.50

B. Based on the calculations, Zhou’s request appears to be a little high. But because the Coefficient of Correlation is only 0.68, it is not very reliable. So we should pay the request until we find a more accurate model. The model is NOT valid.