Business Forecasting 9th Edition Hanke Solutions Manual
richard@qwconsultancy.com
1|Pa ge
The null hypothesis that the mean is still 2.9 is true since the actual mean of the population of data is 2.91 with a standard deviation of 1.608; however, a few students may reject the null hypothesis, committing a Type I error. 11.
a.
b.
Positive linear relationship
c.
Y = 6058 2 X = 513
2
Y = 4,799,724 XY = 48,665
X = 59 r = .938 4
12.
a.
b.
Positive linear relationship
c.
Y = 2312 Y2 = 515,878 X2 = 282.55 XY = 12,029.3
X = 53.7 r = .95
Ŷ = 32.5 + 36.4X Ŷ = 32.5 + 36.4(5.2) = 222
13.
This is a good population for showing how random samples are taken. If three-digit random numbers are generated from Minitab as demonstrated in Problem 10, the selected items for the sample can be easily found. In this population, = 0.06 so most students will get a sample correlation coefficient r close to 0. The least squares line will,
in most cases, have a slope coefficient close to 0, and students will not be able to reject the null hypothesis H0: β1 = 0 (or, equivalently, ρ = 0) if they carry out the hypothesis test.
14.
a. 5
15.
b.
Rent = 275.5 + .518 Size
c.
Slope coefficient = .518 Increase of $.518/month for each additional square foot of space.
d.
Size = 750 Rent = 275.5 + .518(750) = $664/month
n = 175, X = 45 .2, S = 10 .3 Point estimate: X = 45.2 98% confidence interval: 1− = .98 Z = 2.33 X 2.33 S / n = 45.2 2.33 10.3 / 175 = 45.2 1.8 (43.4, 47.0)
(
)
(
)
Hypothesis test: H 0 : = 44 two-sided test, = .02, critical value: |Z|= 2.33 H 1 : 44 Test statistic: Z =
X − 44 S/ n
=
45.2 − 44 10.3 / 175
= 1.54
Since |Z| = 1.54 < 2.33, do not reject H 0 at the 2% level. As expected, the results of the hypothesis test are consistent with the confidence interval for ; = 44 is not ruled out by either procedure.
6
16.
a.
b.
c. 17.
H 0 : = 63,700 H1 : 63,700 H 0 : = 4.3 H1 : 4.3 H 0 : = 1300 H1 : 1300
Large sample 95% confidence interval for mean monthly return μ: − 1.10 1.96
5.99 = −1.10 1.88 39
(−2.98, .78 )
μ = .94 (%) is not a realistic value for mean monthly return of client’s account since it falls outside the 95% confidence interval. Client may have a case. 18.
a.
b.
r = .581, positive linear association between wages and length of service. Other variables affecting wages may be size of bank and previous experience.
c.
WAGES = 324.3 + 1.006 LOS WAGES = 324.3 + 1.006 (80) = 405 7
explain it to her father. CASE 4-5: FIVE-YEAR REVENUE PROJECTION FOR DOWNTOWN RADIOLOGY This case is designed to emphasize the use of subjective probability estimates in a forecasting situation. The methodology used to generate revenue forecasts is both appropriate and accurately employed. The key to answering the question concerning the accuracy of the projections hinges on the accuracy of the assumptions made and estimates used. Examination of the report indicates that the analysts were conservative each time they made an assumption or computed an estimate. This is probably one of the major reasons why the Professional Marketing Associates’ (PMA) forecast is considerably lower. Since we do not know how the accountant projected the number of procedures, it is difficult to determine why his revenue projections were higher. However, it is reasonable to assume that his forecast of the number of cases for each type of procedure was not nearly as sophisticated or thorough as PMAs. Therefore, the recommendation to management should indicate that the PMA forecast, while probably on the conservative side, is more likely to be accurate. Downtown Radiology evidently agreed with PMA's forecast. They decided not to purchase a 9,800 series CT scanner. They also decided to purchase a less expensive MRI. Finally, they decided to obtain outside funding and did not resort to any type of public offering. They built their new imaging center, purchased an MRI and have created a very successful imaging center. CASE 4-6: WEB RETAILER 1.
The time series plot for Orders shows a slight upward trend and a seasonal pattern with peaks in December. Because of the relatively small data set, the autocorrelations are only computed for a limited number of lags, 6 in this case. Consequently with monthly data, the seasonality does not show up in the autocorrelation function. There is significant positive autocorrelation at lag 1, so Orders in consecutive months are correlated. The time series plot for CPO shows a downward trend but a seasonal component is not readily apparent. There is significant positive autocorrelation at lag 1 and the autocorrelations die out relatively slowly. The CPO series is nonstationary and observations in consecutive time periods are correlated.
2.
Winters’ multiplicative smoothing with α = β = γ = .1 works well (see plot below). Forecasts for the next 4 months follow. Residual autocorrelation function below has no significant autocorrelations. Month Forecast Lower Upper Jul/2003 3524720 3072265 3977174 Aug/2003 3885780 3431589 4339972 Sep/2003 3656581 3200544 4112618 Oct/2003 4141277 3683287 4599266
50
3.
Simple exponential smoothing with α = .77 (the optimal α in Minitab) represents the the CPO data well but, like any “averaging” procedure, produces flat-line forecasts. Forecasts of CPO for the next 4 months are: Month Forecast Lower Upper Jul/2003 0.1045 0.0787 0.1303 Aug/2003 0.1045 0.0787 0.1303 Sep/2003 0.1045 0.0787 0.1303 Oct/2003 0.1045 0.0787 0.1303 The results for simple exponential smoothing are pictured below. There are no significant residual autocorrelations (see plot below). 51
4.
Multiplying the Orders forecasts in 2 by the CPO forecasts in 3 gives the Contacts forecasts:
Month
Forecast 52
Jul/2003 Aug/2003 Sep/2003 Oct/2003
368333 406064 382113 432763
5.
It seems reasonable to forecast Contacts directly if the data are available. Multiplying a forecast of Orders by a forecast of CPO to get a forecast of Contacts has the potential for introducing additional error (uncertainty) into the process.
6.
It may or may not be better to focus on the number of units and contacts per unit to get a forecast of contacts. It depends on the nature of the data (ease of modeling) and the amount of relevant data available.
CASE 4-7: SOUTHWEST MEDICAL CENTER 1.
Autocorrelation function for total visits suggests time series is nonstationary (since autocorrelations slow to die out) and seasonal (relatively large autocorrelation at lag 12).
2.
There is no adequate smoothing method to represent Mary’s data. Winters’ multiplicative smoothing with α = β = .5 and γ = .2 seems to do as well as any smoothing procedure (see error measures in plot below). Forecasts for the remainder of FY2003-04 generated by Winters’ procedure follow. Month Forecast Mar/2004 1465.8 Apr/2004 1490.5 May/2004 1453.7 Jun/2004 1465.4 Jul/2004 1568.7 Aug/2004 1552.7
Lower Upper 1249.9 1681.7 1252.6 1728.4 1189.3 1718.1 1171.2 1759.6 1242.3 1895.1 1192.4 1913.0
Forecasts seem high. Residual autocorrelation function pictured below indicates some remaining significant autocorrelation not captured by Winters’ method.
53
The regression equation is LnComp = 5.69 - 0.505 Educate + 0.255 LnSales - 0.0246 PctOwn Predictor Constant Educate LnSales PctOwn S = 0.4953
Coef 5.6865 -0.5046 0.2553 -0.0246
SE Coef 0.6103 0.1170 0.0725 0.0130
R-Sq = 42.8%
T P 9.32 0.000 -4.31 0.000 3.52 0.001 -1.90 0.064
VIF 1.0 1.0 1.0
R-Sq(adj) = 39.1%
Coefficient on education is negative. Everything else equal, as education level increases, compensation decreases. Positive coefficient on lnsales implies as sales increase, compensation increases, everything else equal. Finally, for fixed education and sales, as percent ownership increases, compensation decreases. Unusual Observations Obs Educate LnComp 31 2.00 6.5338 33 0.00 6.3969
Fit 5.9055 7.0645
SE Fit 0.4386 0.2624
Residual St Resid 0.6283 2.73RX -0.6676 -1.59 X
R denotes an observation with a large standardized residual X denotes an observation whose X value gives it large influence. Observation 31 has a large standardized residual and is influential. Observation 33 is also influential. The CEO’s for companies 31 and 33 own relatively large percentages of their company’s stock, 34 % and 17% respectively. They are outliers in this respect. The large residual for company 31 results from underpredicting compensation for this CEO. This CEO receives very adequate compensation in addition to owning a large percentage of the company’s stock. All in all, this k = 3 predictor model appears to be better than the k = 2 predictor model of Example 7.12.
21.
Scatter diagram with fitted quadratic regression function:
135
a. & b. The regression equation is Assets = 7.61 - 0.0046 Accounts + 0.000034 Accounts**2 Predictor Constant Accounts Accounts**2
Coef 7.608 -0.00457 0.00003361
E Coef T P VIF 8.503 0.89 0.401 0.02378 -0.19 0.853 25.965 0.00000893 3.76 0.007 25.965
S = 12.4117 R-Sq = 97.9% R-Sq(adj) = 97.3% Analysis of Variance Source DF SS Regression 2 51130 Residual Error 7 1078 Total 9 52208
MS 25565 154
F 165.95
P 0.000
The regression is significant (F = 165.95, p value = .000). Given Accounts in the model, Accounts**2 is significant ( t value = 3.76, p value = .007). Here Accounts could be dropped from the regression function and the analysis repeated with only Accounts**2 as the predictor variable. If this is done, R2 and the coefficient of Accounts**2 remain virtually unchanged. c. Dropping Accounts**2 from the model gives:
The regression equation is Assets = - 17.1 + 0.0832 Accounts 136
Predictor Coef SE Coef T P Constant -17.121 8.778 -1.95 0.087 Accounts 0.083205 0.007592 10.96 0.000 S = 20.1877 R-Sq = 93.8% R-Sq(adj) = 93.0% The coefficient of Accounts changes from the quadratic model to the straight line model because, not surprisingly, Accounts and Accounts**2 are highly collinear (VIF = 25.965 in the quadratic model). 22.
The final model: The regression equation is Taste = - 30.7 + 4.20 H2S + 17.5 Lactic Predictor Coef SE Coef Constant -30.733 9.146 H2S 4.202 1.049 Lactic 17.526 8.412
T P VIF -3.36 0.006 4.01 0.002 2.019 2.08 0.059 2.019
S = 6.52957 R-Sq = 84.4% R-Sq(adj) = 81.8% Analysis of Variance Source DF SS MS Regression 2 2777.0 1388.5 Residual Error 12 511.6 42.6 Total 14 3288.7
F 32.57
P 0.000
The regression is significant (F = 32.57, p value = .000). Although Lactic is not a significant predictor at the 5% level, it is at the 6% level (t = 2.08, p value = .059) and we have chosen to keep it in the model. R2 indicates about 84% of the variation in Taste is explained by H2S and Lactic. The residual plots below indicate the fitted function is adequate. There is no reason to doubt the usual regression assumptions.
137
23.
Using the final model from problem 22 with H2S = 7.3 and Lactic = 1.85 Predicted Values for New Observations New Obs Fit SE Fit 1 32.36 3.02
95% CI (25.78, 38.95)
95% PI (16.69, 48.04)
Since s y x ' s = 6.53 and t.025 = 2.179 a large sample 95% prediction interval is: 32.36 2.179(6.53) → (18.13, 46.59)
Notice the large sample 95% prediction interval is not too much different than the actual 95% prediction interval (PI) above. Although the fit in this case is relatively good, the standard error of the estimate is somewhat large, so there is a fair amount of uncertainty associated with any forecast. It may be a good idea to collect more data and, perhaps, investigate additional predictor variables.
24.
a. Correlations: GtReceit, MediaRev, StadRev, TotRev, PlayerCt, OpExpens, ... 138
ARIMA model for Yt Final Estimates of Parameters Type Coef StDev T MA 1 -0.3714 0.1052 -3.53 Differencing: 1 regular difference Number of observations: Original series 80, after differencing 79 Residuals: SS = 10637.3 (backforecasts excluded) MS = 136.4 DF = 78 Modified Box-Pierce (Ljung-Box) Chi-Square statistic Lag 12 24 36 48 Chi-Square 9.2(DF=11) 14.1(DF=23) 28.6(DF=35) 39.2(DF=47) Period 81 82 83
95 Percent Limits Lower Upper 245.848 291.635 229.885 307.597 218.787 318.695
Forecast 268.741 268.741 268.741
The critical 5% chi-square value for 11 df's is 19.68. Since the calculated chi-square Q for the residual autocorrelations equals 9.2, the model is deemed adequate. 11.
The slow decline in the early, non-seasonal lags indicates the need for regular differencing. Autocorrelation Function for Yt 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0
2
12
Lag
Corr
T
LBQ
1
0.71
6.92
49.43
2
0.63
4.34
88.66
3
0.63
4
Lag
Corr
T
22
LBQ
Lag
Corr
8 0.54
2.07 309.89
15
9 0.50
1.85 337.18
16
3.69 128.66
10 0.45
1.61 359.38
0.62
3.23 168.41
11 0.50
5
0.63
2.98 210.04
6
0.56
2.41 242.61
7
0.59
2.39 279.06
LBQ
Lag
Corr
0.40
1.22 506.38
22
0.23 0.64 602.29
0.40
1.20 525.09
23
0.26 0.73 610.88
17
0.42
1.26 546.38
24
0.42 1.18 634.13
1.74 387.14
18
0.33
0.97 559.60
12 0.70
2.34 441.38
19
0.35
1.03 574.97
13 0.49
1.56 468.47
20
0.30
0.87 586.38
14 0.41
1.28 487.93
21
0.27
0.78 595.80
181
T
T
LBQ
Autocorrelation Function for Regular 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0
5
Lag
Corr
T
LBQ
1 -0.35 -3.44 2 -0.17 -1.49 3
15
Lag
Corr
25
T
LBQ
Lag
T
LBQ
Lag
12.19
8 -0.01 -0.11
25.78
15 -0.03 -0.19
90.84
22 -0.13 -0.72 109.87
15.08
9 0.05
0.40
26.06
16 -0.05 -0.28
91.10
23 -0.25 -1.43 118.13
0.07
15.09
10 -0.17 -1.35
29.20
17 0.25
98.33
24
4 -0.03 -0.23
15.16
11 -0.29 -2.22
38.14
18 -0.24 -1.38 105.13
5
1.57
18.65
12 0.65
4.80
85.04
19 0.14
6 -0.21 -1.78
23.41
13 -0.19 -1.14
89.05
20 -0.02 -0.14 107.52
7
25.76
14 -0.12 -0.73
90.72
21 0.05
0.01
0.18
0.15
1.21
Corr
1.47
Corr
T
LBQ
0.54 2.98 156.06
25 -0.14 -0.71 158.67
0.79 107.44
0.26 107.79
The peaks at lags 12 and 24 are apparent. The seasonal autocorrelation coefficients seem to be decaying slowly. Seasonal differencing is necessary. The autocorrelation coefficient and partial autocorrelation coefficient plots for the regular and seasonal differenced data are shown on the next page.
182
Autocorrelation Function for Seasonal 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0
5
Lag
Corr
T
LBQ
1 -0.49 -4.44
20.42
2 -0.03 -0.19 3 0.04 0.30
15
Lag
Corr
25
T
LBQ
Lag
T
LBQ
Lag
T
LBQ
8 0.07 0.48
23.42
15 -0.03 -0.15
61.85
22 0.02 0.12
70.43
20.47
9 0.01 0.08
23.43
16 -0.11 -0.66
63.13
23 -0.02 -0.12
70.48
20.61
10 -0.07 -0.50
23.89
17 0.21 1.22
67.63
24 0.02 0.10
70.51
4 0.03 0.23
20.70
11 0.27 2.00
31.19
18 -0.13 -0.78
69.58
25 0.03 0.20
70.65
5 -0.10 -0.76
21.64
12 -0.50 -3.48
55.77
19 0.07 0.40
70.11
6 0.09 0.67
22.38
13 0.24 1.45
61.38
20 -0.05 -0.28
70.36
7 -0.08 -0.62
23.02
14 0.06 0.37
61.78
21 -0.01 -0.07
70.38
Corr
Corr
Partial Autocorrelation Function for Seasonal 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0
5
Lag
15
25
PAC
T
Lag PAC
T
Lag PAC
T
1 -0.49
-4.44
8 -0.07
-0.66
15 -0.04
2 -0.34
-3.14
9 -0.01
-0.07
16 -0.09
3 -0.21
-1.95
10 -0.09
-0.79
17
4 -0.09
-0.81
11
0.34
3.10
5 -0.17
-1.55
12 -0.32
-2.92
6 -0.07
-0.64
13 -0.20
7 -0.15
-1.36
14 -0.12
PAC
T
-0.37
22 -0.04
-0.38
-0.81
23
0.15
1.36
0.01
0.09
24 -0.20
-1.79
18
0.04
0.36
25 -0.05
-0.47
19
0.01
0.09
-1.86
20
0.02
0.17
-1.06
21
0.02
0.19
183
Lag
Concentrating on the non-seasonal lags, the autocorrelation coefficients drop off after one time lag and the partial autocorrelation coefficients trail off, so a regular moving average term of order 1 is indicated. Concentrating on the seasonal lags (12 and 24), the autocorrelation coefficients cut off after lag 12 and the partial autocorrelation coefficients trail off, so a seasonal moving average term of order 12 is suggested. An ARIMA(0,1,1)(0,1,1) model for Yt is identified. Final Estimates of Parameters Type Coef StDev MA 1 0.7486 0.0742 SMA 12 0.8800 0.0893
T 10.09 9.85
Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 96, after differencing 83 Residuals: SS = 5744406210 (backforecasts excluded) MS = 70918595 DF = 81 Modified Box-Pierce (Ljung-Box) Chi-Square statistic Lag 12 24 36 48 Chi-Square 3.0(DF=10) 19.3(DF=22) 23.0(DF=34) 25.1(DF=46) Period 97 98 99 100 101 102 103 104 105 106 107 108
Forecast 163500 158300 177084 178792 188706 184846 191921 188746 185194 187669 188084 221521
95 Percent Limits Lower Upper 146991 180009 141277 175322 159562 194606 160785 196798 170227 207185 165907 203785 172532 211310 168918 208574 164936 205451 166991 208348 166993 209175 200025 243016
The critical 5% chi-square value for 10 df's is 18.31. Since the calculated chi-square Q for the residual autocorrelations equals 3, the model is deemed adequate. 12.
a. See part b. b. The autocorrelation coefficient plot below indicates that the data are non-stationary. Therefore, the data should be first differenced. The autocorrelation coefficient and partial autocorrelation coefficient plots for the first differenced data are also shown.
184
1.
These articles are more abundant than many realize. More "popular” journals, particularly financial markets titles such as Technical Analysis of Stocks & Commodities, Financial Analysts Journal, and Futures present several articles. In addition, the proceedings from the neural network conferences (published by IEEE) will usually have some business applications. Finally, this approach is beginning to appear in more scholarly journals such as Management Science and Decision Sciences.
2.
The interested student with access to a neural network simulator should enjoy this assignment. In addition to the "backpropagation" approach, students might try radial basis functions and least mean squares if they are available.
3.
Model specification is as much an art as it is a science. for example, look at Case 9-4 where the choice between ARIMA(1,1,0) and AR(2) models is not clearcut. Neural networks, however, do not require the analyst to specify the form of the model -- they have been called "model free" function approximators (see Bart Kosko, Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence, Prentice-Hall, 1992, for example).
CHAPTER 11 MANAGING THE FORECASTING PROCESS 225
ANSWERS TO PROBLEMS AND CASES
1.
a. One response: Forecasts may not be right, but they improve the odds of being close to right. More importantly, if there are no agreed upon set of forecasts to drive planning, then different groups may develop own procedures to guide planning with potential chaos as the result. b. One response: Analogy—If you think education is expensive, try ignorance. Having a good set of forecasts is like walking while looking ahead instead of at your shoes. Planning without forecasts will lead to inefficient operations, sub optimal returns on investment, poor customer service, and so forth. c. One response: Good forecasts require not only good quantitative skills, they also require an in-depth understanding of the business or, more generally, the forecasting environment and, ultimately, good communication skills to sell forecasts to management.
CASE 11-1: BOUNDARY ELECTRONICS 1.
This case invites students to think about how to use some of the forecasting techniques discussed in Chapter 11. Guy Preston is trying to get his managers to think about the long-range position of the company, as opposed to the short range thinking that most managers are involved in on a daily basis. The case might generate a class discussion about the tendency of managers to shorten their planning horizons too much in the daily press of business. Guy has asked his managers to write scenarios for the future: a worst case, a status quo, and a most likely scenario. His next task might be to discuss each of these three possibilities, and to discuss any differences of opinion that might emerge. A second round of written scenarios by each participant could then follow this.
2.
The instructor should point out that the purpose of Guy's retreat is to expand the planning horizon of his managers. He should be prepared to continue this effort after the first round of written scenarios: it is quite possible that his team is still caught up in the affairs of the day and is not really engaged in long range thinking. He should encourage expanded thinking after the discussion phase and try during the day to continue such thinking.
3.
There are two possible benefits from Guy's retreat. First, he may gain valuable insights into the company's future to use in his own long range thinking. Second, and probably more important, his managers may come away with an increased awareness of the importance of expanding their planning horizons. If this is true, the company will probably be in a better position to face the future. 226
CASE 11-2: BUSBY ASSOCIATES 1.
Since Holt’s linear smoothing incorporates simple exponential smoothing as a special case (β = 0), would expect Holt’s procedure to fit and forecast better here. Therefore, there is no reason to consider a combination of forecasts. Combining forecasts is best considered when the sets of forecasts are produced by different procedures.
2.
Jill should definitely update her historical data as new data points arrive. Since she is using a computer program to do the forecasting, there would be very little effort involved in this process. Why not update and re-run every quarter for a while?
3.
After the results for a few additional quarters (say 4) become available, the analysis can be re-done to see if the current model is still viable. Model parameters can be re-estimated after each new observation if appropriate computer software is available.
4.
Box-Jenkins ARIMA methodology is not well suited for small sample sizes and can be difficult to explain to a non-statistician. This case illustrates the practical problems that are typically encountered when attempting to forecast a time series in a business setting. Among the problems Jill encounters are: • She chooses to forecast a national variable for which data values are available in the Survey of Current Business. Will this variable correlate well with the actual Y value of interest (her firm's export sales)? • Her initial sample size is only 13. • When she attempts to gather more data, she finds that the series underwent a definition change during the recent past, resulting in inconsistent data. She must shift her focus to another surrogate variable. • Her data plot indicates a bump in the data and she decides a more consistent series would result if she dropped the first few data points. A real life-forecasting project could very likely involve difficulties such as those Jill encountered in this case, or perhaps even more. For this reason this case is a "good read" for forecasting students as they finish their studies since it shows that judgment and skill must be involved in the forecasting effort: forecasting problems are not usually as clean and straightforward as textbook problems.
CASE 11-3: CONSUMER CREDIT COUNSELING Students should summarize the results of the analyses of these data in the cases at the ends of chapters 4 (smoothing), 5 (decomposition), 6 (simple linear regression), 8 (regression with time series data) and 9 (Box-Jenkins methods). Fits, residual analyses, and forecasts can be compared. Regardless of the method, there is a fair amount of unexplained variation in the number of new clients. This may be a situation where combining forecasts makes sense. 227
CASE 11-4: MR. TUX We collected the data from the Mr. Tux rental shop so that real data could be used at the end of each chapter instead of contrived data. We didn't know what would happen when we tried to forecast this variable, but we think it turned out well because no one method was superior. The case in Chapter 11 summarizes the different ways John used to forecast his monthly sales, and asks students to comment on his efforts. We think a key point is that a lot of real data sets do not lend themselves to accurate forecasting, and that continually trying different methods is required. For the Mr. Tux data, there are fairly simple seasonal models (see the cases in Chapters 8 and 9) that represent the data well and provide reasonable forecasts. What advice should we give to John Mosby for the future? Some suggestions to offer might include: 1. Update the data set as future monthly values become available and re-run the most promising analyses to see if the current forecasting model is still viable. 2. Consider combining forecasts from two different methods. 3. Try to develop a useful relationship between monthly sales and regional economic variables. Perhaps the area unemployment rate or an economic activity index would correlate well with John's sales. Perhaps some demographic variables would correlate well. If several variables were collected over the months of John's sales data, a good regression equation might result. This would allow John to understand how is sales are tied to the local environment.
CASE 11-5: ALOMEGA FOOD STORES 1.
Julie has to choose between two different methods of forecasting her company’s monthly sales. Students should review the results of these two efforts and decide which offers the better choice. We find that class presentations by student teams are valuable as they move the analysis beyond the computer results to simulate implementing these results in a “real” situation.
2.
Having students, either individually or in teams, prepare a memo to Julie outlining their analysis and choice of forecasting method is an alternative to class presentations. Again, the results of this case do not point to a “right” answer, but rather to the necessity of choosing a forecasting method and justifying its use. Nonquantitative considerations should come into play: the fact that Julie is the first female president of Alomega, that she jumped over several qualified candidates for the job, and that one of her subordinates (Jackson Tilson) seems to be unimpressed with both her and any computer analysis.
3.
Other forecasting methods are certainly possible in this case. An assignment 228