Problem Set #3 Key Sonoma State University Business 581E Dr. Cuellar The data set bus581e_ps3.dta is a Stata data set containing annual sales (cases) and revenue from December 18, 2004 to April 2 2011. Use Stata and Excel to answer following questions. Your typed answers are due at the beginning of the next class. Answers must be presented in a professional manner for full credit. You may want to export your data into Excel to generate graphs for aesthetic purposes. Forecasting 1. Sales a. Show graphically sales for the entire time span. b. Construct a regression model of sales that accounts for a time trend in sales and seasonal variations. Show and explain your results. Cases = β 0 + β 1time 12 + DMonth k +u i k=2 β k c. Show graphically your predicted results along with your actual sales. Total Cases Sold 20000 30000 40000 50000 60000 70000 01jan2005 01jul2006 01jan2008 01jul2009 01jan2011 Date Actual Predicted
d. Re-run your regression on a sub-sample (hold-out sample) of your data. Hold out the last 13 periods. Show and explain your results. Compare with your regression results from the full sample. Full Sample Hold-Out Sample Cases Cases Time 326.613 317.42 [28.66]** [21.39]** February -11,242.47-10,801.92 [8.53]** [7.53]** March -11,708.08-10,707.84 [8.88]** [7.46]** April -11,161.12-10,218.09 [8.46]** [7.12]** May -14,056.34-13,109.67 [11.30]** [9.47]** June -13,887.43-13,231.25 [10.53]** [9.22]** July -14,935.87-13,840.58 [11.68]** [9.99]** August -15,289.82-14,453.06 [11.14]** [9.60]** September -13,988.94-13,743.68 [10.19]** [9.13]** October -12,204.88-12,054.10 [8.89]** [8.00]** November -7,446.66-6,898.52 [5.42]** [4.58]** December 465.899 853.42 [0.35] [0.59] Constant 35,927.44 35,542.35 [34.45]** [31.27]** Observations 83 70 Adjusted R 2 0.94 0.91 Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level
e. Compare the predictions from your full sample regression with those of the hold-out sample regression. Specifically, compare the difference between actual and predicted results in units and percentage terms. Construct a table as follows: Full Sample Hold-Out Sample Forecast Difference %Difference Forecast Difference %Difference 1-May-10 45060.62-2655.62-6.26% 44969.49-2564.49-6.05% 29-May-10 45387.23 1160.766 2.49% 45286.91 1261.094 2.71% 26-Jun-10 45882.75 221.25 0.48% 45482.75 621.25 1.35% 24-Jul-10 45160.93-3095.93-7.36% 45190.84-3125.84-7.43% 21-Aug-10 45133.59-603.586-1.36% 44895.77-365.773-0.82% 18-Sep-10 46761.09 2399.914 4.88% 45922.57 3238.426 6.59% 16-Oct-10 48871.75 2918.246 5.63% 47929.57 3860.426 7.45% 13-Nov-10 53956.59 977.4141 1.78% 53402.57 1531.426 2.79% 11-Dec-10 62195.76 1833.238 2.86% 61471.94 2557.063 3.99% 8-Jan-11 62056.47 4213.527 6.36% 60935.94 5334.063 8.05% 5-Feb-11 51140.62 1625.383 3.08% 50451.44 2314.563 4.39% 5-Mar-11 51001.62-1677.62-3.40% 50862.94-1538.94-3.12% 2-Apr-11 51875.19-1279.19-2.53% 51670.11-1074.11-2.12% How well does the hold-out sample compare with the full sample results?
f. Use the full sample of data to forecast sales for 13 periods beyond the end of the data. g. Construct a margin of error for your forecast and a 95% confidence interval. Show your results for f & g in a table as follows: Period Forecasted Sales Margin of Error Lower CI Upper CI 1 49306.59 1860.56 47446.03 51167.14 2 49802.11 2131.667 47670.44 51933.77 3 49080.29 2093.376 46986.91 51173.66 4 49052.94 2248.777 46804.16 51301.72 5 50680.44 2248.777 48431.66 52929.22 6 52791.11 2248.777 50542.33 55039.88 7 57875.94 2248.777 55627.16 60124.72 8 66115.12 2191.179 63923.94 68306.3 9 65975.83 2191.179 63784.65 68167.01 10 55059.97 2191.179 52868.79 57251.15 11 54920.97 2191.179 52729.79 57112.15 12 55794.54 2191.179 53603.36 57985.72 13 53225.94 2003.829 51222.11 55229.77 h. Show your results graphically. Be sure your graph clearly distinguishes between actual and predicted values. You may want to use Excel. Total Cases Sold 20000 30000 40000 50000 60000 70000 0 20 40 60 80 100 Date Actual Lower 95% CI Predicted Upper 95% CI
30-Apr-11 28-May-11 25-Jun-11 23-Jul-11 20-Aug-11 17-Sep-11 15-Oct-11 12-Nov-11 10-Dec-11 7-Jan-12 4-Feb-12 3-Mar-12 31-Mar-12 Sales (Cases) 70,000 65,000 Forecasted Sales Lower Confidence Interval Upper Confidence Interval Forecast 60,000 55,000 50,000 45,000
2. Revenue a. Show graphically revenue for the entire time span. b. Construct a regression model of revenue that accounts for a time trend in revenue and seasonal variations. Show and explain your results. Revenue = β 0 + β 1time 12 + DMonth k +u i k=2 β k c. Show graphically your predicted results along with your actual revenue. Revenue 2.0e+06 4.0e+06 6.0e+06 8.0e+06 01jan2005 01jul2006 01jan2008 01jul2009 01jan2011 Date Actual Predicted
d. Re-run your regression on a sub-sample (hold-out sample) of your data. Hold out the last 13 periods. Show and explain your results. Compare with your regression results from the full sample. Full Sample Hold-Out Sample Revenue Revenue Time 41,891.66 42,353.19 [31.11]** [24.08]** February -1331846.375-1272860.185 [8.55]** [7.48]** March -1388236.465-1271334.702 [8.91]** [7.47]** April -1379528.697-1260346.054 [8.85]** [7.40]** May -1703024.547-1572700.858 [11.58]** [9.59]** June -1716002.344-1608645.649 [11.01]** [9.45]** July -1846491.565-1695770.964 [12.22]** [10.33]** August -1868417.563-1753123.544 [11.52]** [9.82]** September -1651441.724-1601510.328 [10.18]** [8.97]** October -1404461.718-1371862.713 [8.66]** [7.68]** November -873,340.71-798,461.10 [5.38]** [4.47]** December 2,430.66 58,715.02 [0.02] [0.35] Constant 4162495.469 4064491.299 [33.78]** [30.16]** Observations 83 70 Adjusted R 2 0.94 0.93 Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level
e. Compare the predictions from your full sample regression with those of the hold-out sample regression. Specifically, compare the difference between actual and predicted results in units and percentage terms. Construct a table as above. Full Sample Hold-Out Sample Forecast Difference %Diff Forecast Difference %Diff 1-May-10 $5,433,779 -$345,910-6.80% $5,498,867 -$410,998-8.08% 29-May-10 $5,475,671 -$2,631-0.05% $5,541,220 -$68,180-1.25% 26-Jun-10 $5,504,585 -$148,882-2.78% $5,547,628 -$191,925-3.58% 24-Jul-10 $5,415,987 -$463,166-9.35% $5,502,856 -$550,035-11.11% 21-Aug-10 $5,435,953 -$169,524-3.22% $5,487,857 -$221,428-4.20% 18-Sep-10 $5,694,820 $154,982 2.65% $5,681,823 $167,979 2.87% 16-Oct-10 $5,983,692 $239,337 3.85% $5,953,824 $269,204 4.33% 13-Nov-10 $6,556,705 $25,626 0.39% $6,569,579 $12,752 0.19% 11-Dec-10 $7,474,368 $157,553 2.06% $7,469,108 $162,812 2.13% 8-Jan-11 $7,513,829 $492,490 6.15% $7,452,746 $553,572 6.91% 5-Feb-11 $6,223,874 $135,804 2.14% $6,222,239 $137,438 2.16% 5-Mar-11 $6,209,375 -$214,459-3.58% $6,266,118 -$271,202-4.52% 2-Apr-11 $6,259,975 -$230,914-3.83% $6,319,460 -$290,399-4.82%
f. Use the full sample of data to forecast sales for 13 periods beyond the end of the data. g. Construct a margin of error for your forecast and a 95% confidence interval. Show your results for f & g in a table as above h. Show your results graphically. Be sure your graph clearly distinguishes between actual and predicted values. You may want to use Excel. Revenue 30-Apr-11 2.0e+06 4.0e+06 6.0e+06 8.0e+06 28-May-11 25-Jun-11 23-Jul-11 20-Aug-11 17-Sep-11 15-Oct-11 12-Nov-11 10-Dec-11 7-Jan-12 4-Feb-12 3-Mar-12 31-Mar-12 Revenue 0 20 40 60 80 100 Date Actual Lower 95% CI Predicted Upper 95% CI $9,000,000 $8,500,000 $8,000,000 Forecasted Revenue Lower Confidence Interval Upper Confidence Interval Forecast $7,500,000 $7,000,000 $6,500,000 $6,000,000 $5,500,000 $5,000,000
Period Forecasted Revenue Margin of Error Lower CI Upper CI 1 $5,978,371 $219,840 $5,758,530 $6,198,211 2 $6,007,285 $251,874 $5,755,411 $6,259,159 3 $5,918,687 $247,349 $5,671,338 $6,166,037 4 $5,938,653 $265,711 $5,672,941 $6,204,364 5 $6,197,520 $265,711 $5,931,809 $6,463,232 6 $6,486,392 $265,711 $6,220,680 $6,752,103 7 $7,059,404 $265,711 $6,793,693 $7,325,116 8 $7,977,068 $258,906 $7,718,162 $8,235,973 9 $8,016,529 $258,906 $7,757,623 $8,275,434 10 $6,726,574 $258,906 $6,467,668 $6,985,479 11 $6,712,075 $258,906 $6,453,170 $6,970,981 12 $6,762,675 $258,906 $6,503,769 $7,021,580 13 $6,481,071 $236,769 $6,244,302 $6,717,839 Use the data set bus581e_ps1 to answer the following questions. 3. Trend Analysis a. Show graphically total cases sold by period for the duration of the data set. b. Calculate the percentage growth rate of total sales using regression analysis. c. Show graphically total cases sold of chardonnay by period for the duration of the data set. d. Calculate the percentage growth rate of total chardonnay sales using regression analysis. Has the growth rate of chardonnay sales been above or below total sales? e. Show graphically total cases of merlot sold by period for the duration of the data set. f. Calculate the percentage growth rate of total merlot sales using regression analysis. Has the growth rate of merlot sales been above or below total sales? g. Show graphically total cases sold of cabernet sauvignon by period for the duration of the data set. h. Calculate the percentage growth rate of total cabernet sauvignon sales using regression analysis. Has the growth rate of merlot sales been above or below total sales? i. Show graphically total cases sold, chardonnay, merlot and cabernet sauvignon sales together. Describe your graph. Regression Results Total Chardonnay Merlot Cabernet Sauvignon time 0.009 0.008 0.005 0.020 [13.31]** [18.59]** [5.11]** [22.18]** Constant 10.181 8.851 9.073 7.467 [324.46]** [435.15]** [212.46]** [174.12]** Observations 83 83 83 83 Adjusted R-squared 0.68 0.81 0.23 0.86 Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level Annual Growth Rate 11.83% 10.65% 6.02% 28.82% Compounding Annual Growth Rate 11.23% 10.16% 5.86% 25.57% Not Compounding
Cases Sold Per 4-week ending period 70,000 Total 60,000 50,000 40,000 30,000 20,000 10,000 0 4-week ending period
Cases Sold Per 4-week ending period 16,000 Chardonnay 14,000 12,000 10,000 8,000 6,000 4,000 2,000 0 4-week ending period
Cases Sold Per 4-week ending period 18,000 16,000 Merlot 14,000 12,000 10,000 8,000 6,000 4,000 2,000 0 4-week ending period
Cases Sold Per 4-week ending period 12,000 Cabernet Sauvignon 10,000 8,000 6,000 4,000 2,000 0 4-week ending period
Cases Sold Per 4-week ending period 70,000 60,000 Chardonnay Merlot Total CB-S 50,000 40,000 30,000 20,000 10,000 0 4-week ending period
Indexed Cases Sold Per 4-week ending period 4. Indexing Trends a. Index total cases sold for the duration of the period and re-graph. Be sure that indexed cases sold are zero in the first period. Interpret your graph. b. Index total cases sold of chardonnay for the duration of the period and re-graph. Be sure that indexed cases sold are zero in the first period. Interpret your graph. c. Index total cases sold of merlot for the duration of the period and re-graph. Be sure that indexed cases sold are zero in the first period. Interpret your graph. d. Index total cases sold of cabernet sauvignon for the duration of the period and re-graph. Be sure that indexed cases sold are zero in the first period. Interpret your graph. e. Show graphically indexed total cases sold, indexed chardonnay, indexed merlot sales and indexed cabernet sauvignon sales together. Interpret your graph. 4.00 3.50 3.00 Chardonnay Merlot Total CB-S 2.50 2.00 1.50 1.00 0.50 0.00-0.50-1.00 4-week ending period