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In: Statistics and Probability

Sales of roof material, by quarter, for 2010 through 2016, by Carolina Home Construction Inc. are...

Sales of roof material, by quarter, for 2010 through 2016, by Carolina Home Construction Inc. are shown below (in $000). Quarter Year I II III IV 2010 69 241 211 220 2011 85 236 249 222 2012 100 284 253 256 2013 117 298 275 268 2014 113 305 309 299 2015 120 311 325 296 2016 130 327 210 183 Click here for the Excel Data File Determine the typical seasonal patterns for sales using the ratio-to-moving-average method. (Round your answers to 4 decimal places.) Deseasonalize the data and determine the trend equation. (Round your answers to 3 decimal places.) Project sales for 2017 using the trend equation and seasonally adjust these values to find the predicted sales for each quarter. (Round your answers to 4 decimal places.)

Solutions

Expert Solution

Centered Moving Average and Deseasonalization
Centered
Moving Ratio to Seasonal Sales
t Year Quarter Sales Average CMA Indexes Deseasonalized
1 1 1 69 0.469 147.194
2 1 2 241 1.251 192.684
3 1 3 211 187.2500 1.1268 1.169 180.549
4 1 4 220 188.6250 1.1663 1.112 197.873
5 2 1 85 192.7500 0.4410 0.469 181.325
6 2 2 236 197.7500 1.1934 1.251 188.687
7 2 3 249 199.8750 1.2458 1.169 213.065
8 2 4 222 207.7500 1.0686 1.112 199.672
9 3 1 100 214.2500 0.4667 0.469 213.324
10 3 2 284 219.0000 1.2968 1.251 227.064
11 3 3 253 225.3750 1.1226 1.169 216.488
12 3 4 256 229.2500 1.1167 1.112 230.252
13 4 1 117 233.7500 0.5005 0.469 249.589
14 4 2 298 238.0000 1.2521 1.251 238.257
15 4 3 275 239.0000 1.1506 1.169 235.313
16 4 4 268 239.3750 1.1196 1.112 241.045
17 5 1 113 244.5000 0.4622 0.469 241.056
18 5 2 305 252.6250 1.2073 1.251 243.853
19 5 3 309 257.3750 1.2006 1.169 264.407
20 5 4 299 259.0000 1.1544 1.112 268.928
21 6 1 120 261.7500 0.4585 0.469 255.989
22 6 2 311 263.3750 1.1808 1.251 248.651
23 6 3 325 264.2500 1.2299 1.169 278.097
24 6 4 296 267.5000 1.1065 1.112 266.229
25 7 1 130 255.1250 0.5096 0.469 277.321
26 7 2 327 226.6250 1.4429 1.251 261.443
27 7 3 210 1.169 179.694
28 7 4 183 1.112 164.594

Predicted Sales for 2017

Quarter I: Sales = 0.469 * [2.5281(29) + 188.44] = 122.7630

Quarter II: Sales = 1.251 * [2.5281(30) + 188.44] = 330.6180

Quarter III: Sales = 1.169 * [2.5281(31) + 188.44] = 311.9022

Quarter IV: Sales = 1.112 * [2.5281(32) + 188.44] = 299.5052

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orchestra answered 2 years ago
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