Question

2:5-34 Resolve Problem 5-33 with a = 0.3. Using MAD, which smoothing constant provides a better forecast? 3:5-35 A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are com- piled, and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data (in $1,000,000s) for one par- ticular area of southeast Texas follow: QUARTER YEAR 1 YEAR 2 YEAR 3 YEAR 4 218 225 250 - a 234 265 254 283 247 243 00 255 264 289 356 292 299 327 + (a) Compute a seasonal index for each quarter based on a CMA. (b) Deseasonalize the data, and develop a trend line on the deseasonalized data. (c) Use the trend line to forecast the sales for each quarter of year 5. (d) Use the seasonal indices to adjust the forecasts found in part (C) to obtain the final forecasts. 35-36 Using the data in Problem 5-35, develop a multiple regression model to predict sales (with both trend and seasonal components), using dummy variables to
please explain your answer.

Answer 1

CMA. Revenues Seasonal ratio Year Q 218 247 0.9686 - d m s 243 250.875 282.625 1.1559 292 255 0.88.24 225 254 0.9689 0 257. Its 259.85 261.875 0.9831 255 1.1418 299 - N M 5 - Nms 234 263.125 265 266.5 0.8893 6.9944 0.9338 1-1837 272 254 327 276.25 I 250 282.875 0.8838 0.9729 290.875 – dm- 283 289 356 Ratios thad used in computing CmAs & 225lors) 1 218(05) +242 +243 +2927. CmA (quenter 3 of year 1) = 218| - 250.875 (mAlqmark 4 of geanta 24710 15) + 2431 242 +225 + 25660-5) - 252.625 & so on. Revenue in quada ] Catior CMA - 250 875 - 6.9686 243 & so on

10.8851 0.8824+0.8893+0.8830 (a) Index (quanton 1) = 0. - > Index (a, 2) = 0.0869 to a que to 1972 - Index (93)= 0.9686 to .9831 to 9378 = 10.9847 0.9619 Index (94) = 1.15594 1.418 1 1837 - - [1.1604 (3) Fornella is! deseasonalized date - Actual revenue Seasonal reneane using the & forrelate the table? Des. Der (7) Time period Quantes Sindler Revenue 218 0.8851 0.9847 246. 2aaa 250.8378 247 dmt 243 297 0.9619 1.1604 252.6250 251.6374 4 254.286 - 225 0.8851 N 254 257.9466 265.2003 0.9847 0.9619 25S ms 299 1.1604 253.6695 234 0.8851 264.3769 2691195 204.3769 265 – d mo 254 or 9847 6.9619 1.1604 281.7194 327 0.8851 250 283 282.4540 287. 1972 3204420 0.9842 – u ms. 289 0.9619 1.1604 306.4908 356

Coefficients Standard Frow t-Stat p-value Intacept 28.6157 3.4541 68.79 o Time periody) 3.609 0.3572 10ill o Trend perjection model is 19 = 237. 6189 +3.60 90x] where } is the predicted suvenue. C) Time period & should be 17, 18, 19, 20. Y = 237.6157 & 3.6092 (A) = 1298.9806] (hor 17) ŷ (18) = 237.6158 +3.6092 (18) = 1302.5903) y (19) = 3002] ŷ (20) = 1309. 68097 (d) Just ventsply by the index ů (P) x Index (91)= 298.9606x0.885, 2989606 X0,8851 - 1284.6292] ý (18) & Index (q) = (297.9600. ý (19) & Index (43) = 1294.52 ♡ (20) & Index (quz 1359.50