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Calculated Shard: 94 (from laksa035)

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curl -X POST \
  'http://laksa094.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_14.html\')), getAhrefsUnparsedNoserviceFromURL(\'https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_14.html\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_14.html","crawl_time":1775526390,"first_indexed_time":1634334599,"http_code":200,"src_unparsed":"edu,psu!worldcampus,courses,\/welcome\/mangt515\/lesson02_14.html s443","src_root_hash":"16520191723648810894","history_drop_reason":null,"meta_title":"Example of Trend-Adjusted Exponential Smoothing","meta_descriptions":[],"attrs_boilerpipe_text":"Example of Trend-Adjusted Exponential Smoothing\nFor the data given below, generate a forecast for period 11 through 13 using trend-adjusted exponential smoothing. Use\n= 0.4 and\n= 0.3\nPeriod\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nData values\n500\n524\n520\n528\n540\n542\n558\n550\n570\n575\nSolution:\nTo use trend adjusted exponential smoothing, we first need an initial estimate of the trend. This initial estimate can be obtained by calculating the net change from the three changes in the data that occurred through the first four periods.\nInitial Trend Estimate = (528 - 500)\/3 = 28\/3 = 9.33\nUsing this initial trend estimate and the actual data value for period 4, we compute an initial forecast for period 5.\nInitial Forecast for period 5 = 528 + 9.33 = 537.33.\nThe forecasts and the associated calculations are shown in the table below.\nTable 2.1 Forecast Calculations for the Trend-Adjusted Exponential Smoothing Example\nPeriod\nActual\nS\nt-1\n+ T\nt-1\n= TAF\nt\nTAF\nt\n+ 0.3(A\nt\n-TAF\nt\n) = S\nt\nT\nt-1\n+ 0.2(TAF\nt\n-TAF\nt-1\n- T\nt-1\n) = T\nt\n5\n540\n528 + 9.33 = 537.33\n537.33 + 0.3(540 - 537.33) = 538.13\n9.33\n6\n542\n538.13 + 9.33 = 547.46\n547.46 + 0.3(542 - 547.46) = 545.82\n9.33 + 0.2(547.46 - 537.33 - 9.33) = 9.49\n7\n558\n545.82 + 9.49 = 555.31\n555.31 + 0.3(558 - 555.31) = 556.12\n9.49 + 0.2(555.31 - 547.46 - 9.49) = 9.16\n8\n550\n556.12 + 9.16 = 565.28\n565.28 + 0.3(550 - 565.28) = 560.70\n9.16 + 0.2(565.28 - 555.31 - 9.16) = 9.32\n9\n570\n560.70 + 9.32 = 570.02\n570.02 + 0.3(570 - 570.02) = 570.01\n9.32 + 0.2(570.02 - 565.28 - 9.32) = 8.41\n10\n575\n570.01 + 8.41 = 578.42\n578.42 + 0.3(575 - 578.42) = 577.40\n8.41 + 0.2(578.42 - 570.02 - 8.41) = 8.41\n11\n577.40 + 8.41 = 585.81\nThe forecast for period 11 is 585.81.","attrs_markdown":"![](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/case_static\/images\/C.jpg)\n\nMANGT 515: Cost and Value Management\n\n[previous](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_13.html) \\| [contents](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/toc.html) \\| [next](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_15.html)\n\nMANGT 515 Prospective Students\n\n|   |\n|---|\n| [Sample Syllabus](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/index.html \"Sample Syllabus\") |\n| [Sample Lesson](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/toc.html \"Sample Lesson\") |\n| [Introduction](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_01.html) |\n| [2\\.1 Reasons for Forecasting in Project Management](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_02.html) |\n| [2\\.2 Forecasting Methods for Projects](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_03.html) |\n| [2\\.2.1 Qualitative Forecasting Methods](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_04.html) |\n| [2\\.2.2 Quantitative Forecasting Methods](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_05.html) |\n| [Time Series Analysis](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_06.html) |\n| [Short Term Forecasting Methods](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_07.html) |\n| [Naïve Approach](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_08.html) |\n| [Simple Averages](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_09.html) |\n| [Moving Averages](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_10.html) |\n| [Exponential Smoothing](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_11.html) |\n| [Example of Exponential Smoothing](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_12.html) |\n| [Trend-Adjusted Exponential Smoothing](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_13.html) |\n| [Example of Trend-Adjusted Exponential Smoothing](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_14.html) |\n| [2\\.3 Intermediate Term Forecasting](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_15.html) |\n| [Example of Linear Regression](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_16.html) |\n| [Evaluating the \"Fit\" of the Regression Line](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_17.html) |\n| [2\\.3.2 The Correlation Coefficient (r)](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_18.html) |\n| [2\\.3.3. The Standard Error of the Estimate (syx)](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_19.html) |\n| [2\\.3.4 Limitations in Forecasting Using Linear Regression](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_20.html) |\n| [2\\.3.4 Limitations in Forecasting Using Linear Regression (continued)](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_21.html) |\n| [2\\.4 Forecasting the Project End Conditions](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_22.html) |\n| [2\\.5 S-curve Forecasting](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_23.html) |\n| [2\\.6 Technological Forecasting\\*](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_24.html) |\n\n### **Example of Trend-Adjusted Exponential Smoothing**\nFor the data given below, generate a forecast for period 11 through 13 using trend-adjusted exponential smoothing. Use ![alpha](https:\/\/courses.worldcampus.psu.edu\/images\/all_lessons\/mangt515_alpha.gif) = 0.4 and ![beta](https:\/\/courses.worldcampus.psu.edu\/images\/all_lessons\/mangt515_beta1.gif) = 0.3\n\n|   |   |   |   |   |   |   |   |   |   |   |\n|---|---|---|---|---|---|---|---|---|---|---|\n| Period | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |\n| Data values | 500 | 524 | 520 | 528 | 540 | 542 | 558 | 550 | 570 | 575 |\n\n**Solution:** To use trend adjusted exponential smoothing, we first need an initial estimate of the trend. This initial estimate can be obtained by calculating the net change from the three changes in the data that occurred through the first four periods.\n\n- Initial Trend Estimate = (528 - 500)\/3 = 28\/3 = 9.33\n\nUsing this initial trend estimate and the actual data value for period 4, we compute an initial forecast for period 5.\n\n- Initial Forecast for period 5 = 528 + 9.33 = 537.33.\n\nThe forecasts and the associated calculations are shown in the table below.\n\n| **Period** | **Actual** | **S**t-1 **\\+ T**t-1 **\\= TAF**t | **TAF**t **\\+ 0.3(A**t **\\-TAF**t **) = S**t | **T**t-1 **\\+ 0.2(TAF**t **\\-TAF**t-1 **\\- T**t-1 **) = Tt** |\n|---|---|---|---|---|\n| 5 | 540 | 528 + 9.33 = 537.33 | 537\\.33 + 0.3(540 - 537.33) = 538.13 | 9\\.33 |\n| 6 | 542 | 538\\.13 + 9.33 = 547.46 | 547\\.46 + 0.3(542 - 547.46) = 545.82 | 9\\.33 + 0.2(547.46 - 537.33 - 9.33) = 9.49 |\n| 7 | 558 | 545\\.82 + 9.49 = 555.31 | 555\\.31 + 0.3(558 - 555.31) = 556.12 | 9\\.49 + 0.2(555.31 - 547.46 - 9.49) = 9.16 |\n| 8 | 550 | 556\\.12 + 9.16 = 565.28 | 565\\.28 + 0.3(550 - 565.28) = 560.70 | 9\\.16 + 0.2(565.28 - 555.31 - 9.16) = 9.32 |\n| 9 | 570 | 560\\.70 + 9.32 = 570.02 | 570\\.02 + 0.3(570 - 570.02) = 570.01 | 9\\.32 + 0.2(570.02 - 565.28 - 9.32) = 8.41 |\n| 10 | 575 | 570\\.01 + 8.41 = 578.42 | 578\\.42 + 0.3(575 - 578.42) = 577.40 | 8\\.41 + 0.2(578.42 - 570.02 - 8.41) = 8.41 |\n| 11 |   | 577\\.40 + 8.41 = 585.81 |   |   |\n\nThe forecast for period 11 is 585.81.\n\npage 14 of 24\n\nPennsylvania State University �2007\n\n[previous](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_13.html) \\| [contents](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/toc.html) \\| [next](https:\/\/courses.worldcampus.psu.edu\/welcome\/mangt515\/lesson02_15.html)","attrs_readable_markdown":"### **Example of Trend-Adjusted Exponential Smoothing**\nFor the data given below, generate a forecast for period 11 through 13 using trend-adjusted exponential smoothing. Use ![alpha](https:\/\/courses.worldcampus.psu.edu\/images\/all_lessons\/mangt515_alpha.gif) = 0.4 and ![beta](https:\/\/courses.worldcampus.psu.edu\/images\/all_lessons\/mangt515_beta1.gif) = 0.3\n\n|   |   |   |   |   |   |   |   |   |   |   |\n|---|---|---|---|---|---|---|---|---|---|---|\n| Period | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |\n| Data values | 500 | 524 | 520 | 528 | 540 | 542 | 558 | 550 | 570 | 575 |\n\n**Solution:** To use trend adjusted exponential smoothing, we first need an initial estimate of the trend. This initial estimate can be obtained by calculating the net change from the three changes in the data that occurred through the first four periods.\n\n- Initial Trend Estimate = (528 - 500)\/3 = 28\/3 = 9.33\n\nUsing this initial trend estimate and the actual data value for period 4, we compute an initial forecast for period 5.\n\n- Initial Forecast for period 5 = 528 + 9.33 = 537.33.\n\nThe forecasts and the associated calculations are shown in the table below.\n\n| **Period** | **Actual** | **S**t-1 **\\+ T**t-1 **\\= TAF**t | **TAF**t **\\+ 0.3(A**t **\\-TAF**t **) = S**t | **T**t-1 **\\+ 0.2(TAF**t **\\-TAF**t-1 **\\- T**t-1 **) = Tt** |\n|---|---|---|---|---|\n| 5 | 540 | 528 + 9.33 = 537.33 | 537\\.33 + 0.3(540 - 537.33) = 538.13 | 9\\.33 |\n| 6 | 542 | 538\\.13 + 9.33 = 547.46 | 547\\.46 + 0.3(542 - 547.46) = 545.82 | 9\\.33 + 0.2(547.46 - 537.33 - 9.33) = 9.49 |\n| 7 | 558 | 545\\.82 + 9.49 = 555.31 | 555\\.31 + 0.3(558 - 555.31) = 556.12 | 9\\.49 + 0.2(555.31 - 547.46 - 9.49) = 9.16 |\n| 8 | 550 | 556\\.12 + 9.16 = 565.28 | 565\\.28 + 0.3(550 - 565.28) = 560.70 | 9\\.16 + 0.2(565.28 - 555.31 - 9.16) = 9.32 |\n| 9 | 570 | 560\\.70 + 9.32 = 570.02 | 570\\.02 + 0.3(570 - 570.02) = 570.01 | 9\\.32 + 0.2(570.02 - 565.28 - 9.32) = 8.41 |\n| 10 | 575 | 570\\.01 + 8.41 = 578.42 | 578\\.42 + 0.3(575 - 578.42) = 577.40 | 8\\.41 + 0.2(578.42 - 570.02 - 8.41) = 8.41 |\n| 11 |   | 577\\.40 + 8.41 = 585.81 |   |   |\n\nThe forecast for period 11 is 585.81.","meta_canonical":null}

3. Robots.txt Check

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Filter	Status	Condition	Details
HTTP status	PASS	`download_http_code = 200`	HTTP 200
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URL	https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_14.html
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Boilerpipe Text	Example of Trend-Adjusted Exponential Smoothing For the data given below, generate a forecast for period 11 through 13 using trend-adjusted exponential smoothing. Use = 0.4 and = 0.3 Period 1 2 3 4 5 6 7 8 9 10 Data values 500 524 520 528 540 542 558 550 570 575 Solution: To use trend adjusted exponential smoothing, we first need an initial estimate of the trend. This initial estimate can be obtained by calculating the net change from the three changes in the data that occurred through the first four periods. Initial Trend Estimate = (528 - 500)/3 = 28/3 = 9.33 Using this initial trend estimate and the actual data value for period 4, we compute an initial forecast for period 5. Initial Forecast for period 5 = 528 + 9.33 = 537.33. The forecasts and the associated calculations are shown in the table below. Table 2.1 Forecast Calculations for the Trend-Adjusted Exponential Smoothing Example Period Actual S t-1 + T t-1 = TAF t TAF t + 0.3(A t -TAF t ) = S t T t-1 + 0.2(TAF t -TAF t-1 - T t-1 ) = T t 5 540 528 + 9.33 = 537.33 537.33 + 0.3(540 - 537.33) = 538.13 9.33 6 542 538.13 + 9.33 = 547.46 547.46 + 0.3(542 - 547.46) = 545.82 9.33 + 0.2(547.46 - 537.33 - 9.33) = 9.49 7 558 545.82 + 9.49 = 555.31 555.31 + 0.3(558 - 555.31) = 556.12 9.49 + 0.2(555.31 - 547.46 - 9.49) = 9.16 8 550 556.12 + 9.16 = 565.28 565.28 + 0.3(550 - 565.28) = 560.70 9.16 + 0.2(565.28 - 555.31 - 9.16) = 9.32 9 570 560.70 + 9.32 = 570.02 570.02 + 0.3(570 - 570.02) = 570.01 9.32 + 0.2(570.02 - 565.28 - 9.32) = 8.41 10 575 570.01 + 8.41 = 578.42 578.42 + 0.3(575 - 578.42) = 577.40 8.41 + 0.2(578.42 - 570.02 - 8.41) = 8.41 11 577.40 + 8.41 = 585.81 The forecast for period 11 is 585.81.
Markdown	![](https://courses.worldcampus.psu.edu/welcome/mangt515/case_static/images/C.jpg) MANGT 515: Cost and Value Management [previous](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_13.html) \\| [contents](https://courses.worldcampus.psu.edu/welcome/mangt515/toc.html) \\| [next](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_15.html) MANGT 515 Prospective Students \| \| \|---\| \| [Sample Syllabus](https://courses.worldcampus.psu.edu/welcome/mangt515/index.html "Sample Syllabus") \| \| [Sample Lesson](https://courses.worldcampus.psu.edu/welcome/mangt515/toc.html "Sample Lesson") \| \| [Introduction](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_01.html) \| \| [2\.1 Reasons for Forecasting in Project Management](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_02.html) \| \| [2\.2 Forecasting Methods for Projects](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_03.html) \| \| [2\.2.1 Qualitative Forecasting Methods](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_04.html) \| \| [2\.2.2 Quantitative Forecasting Methods](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_05.html) \| \| [Time Series Analysis](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_06.html) \| \| [Short Term Forecasting Methods](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_07.html) \| \| [Naïve Approach](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_08.html) \| \| [Simple Averages](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_09.html) \| \| [Moving Averages](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_10.html) \| \| [Exponential Smoothing](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_11.html) \| \| [Example of Exponential Smoothing](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_12.html) \| \| [Trend-Adjusted Exponential Smoothing](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_13.html) \| \| [Example of Trend-Adjusted Exponential Smoothing](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_14.html) \| \| [2\.3 Intermediate Term Forecasting](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_15.html) \| \| [Example of Linear Regression](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_16.html) \| \| [Evaluating the "Fit" of the Regression Line](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_17.html) \| \| [2\.3.2 The Correlation Coefficient (r)](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_18.html) \| \| [2\.3.3. The Standard Error of the Estimate (syx)](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_19.html) \| \| [2\.3.4 Limitations in Forecasting Using Linear Regression](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_20.html) \| \| [2\.3.4 Limitations in Forecasting Using Linear Regression (continued)](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_21.html) \| \| [2\.4 Forecasting the Project End Conditions](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_22.html) \| \| [2\.5 S-curve Forecasting](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_23.html) \| \| [2\.6 Technological Forecasting\](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_24.html) \| ### Example of Trend-Adjusted Exponential Smoothing* For the data given below, generate a forecast for period 11 through 13 using trend-adjusted exponential smoothing. Use ![alpha](https://courses.worldcampus.psu.edu/images/all_lessons/mangt515_alpha.gif) = 0.4 and ![beta](https://courses.worldcampus.psu.edu/images/all_lessons/mangt515_beta1.gif) = 0.3 \| \| \| \| \| \| \| \| \| \| \| \| \|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\| \| Period \| 1 \| 2 \| 3 \| 4 \| 5 \| 6 \| 7 \| 8 \| 9 \| 10 \| \| Data values \| 500 \| 524 \| 520 \| 528 \| 540 \| 542 \| 558 \| 550 \| 570 \| 575 \| Solution: To use trend adjusted exponential smoothing, we first need an initial estimate of the trend. This initial estimate can be obtained by calculating the net change from the three changes in the data that occurred through the first four periods. - Initial Trend Estimate = (528 - 500)/3 = 28/3 = 9.33 Using this initial trend estimate and the actual data value for period 4, we compute an initial forecast for period 5. - Initial Forecast for period 5 = 528 + 9.33 = 537.33. The forecasts and the associated calculations are shown in the table below. \| Period \| Actual \| St-1 \+ Tt-1 \= TAFt \| TAFt \+ 0.3(At \-TAFt ) = St \| Tt-1 \+ 0.2(TAFt \-TAFt-1 \- Tt-1 ) = Tt \| \|---\|---\|---\|---\|---\| \| 5 \| 540 \| 528 + 9.33 = 537.33 \| 537\.33 + 0.3(540 - 537.33) = 538.13 \| 9\.33 \| \| 6 \| 542 \| 538\.13 + 9.33 = 547.46 \| 547\.46 + 0.3(542 - 547.46) = 545.82 \| 9\.33 + 0.2(547.46 - 537.33 - 9.33) = 9.49 \| \| 7 \| 558 \| 545\.82 + 9.49 = 555.31 \| 555\.31 + 0.3(558 - 555.31) = 556.12 \| 9\.49 + 0.2(555.31 - 547.46 - 9.49) = 9.16 \| \| 8 \| 550 \| 556\.12 + 9.16 = 565.28 \| 565\.28 + 0.3(550 - 565.28) = 560.70 \| 9\.16 + 0.2(565.28 - 555.31 - 9.16) = 9.32 \| \| 9 \| 570 \| 560\.70 + 9.32 = 570.02 \| 570\.02 + 0.3(570 - 570.02) = 570.01 \| 9\.32 + 0.2(570.02 - 565.28 - 9.32) = 8.41 \| \| 10 \| 575 \| 570\.01 + 8.41 = 578.42 \| 578\.42 + 0.3(575 - 578.42) = 577.40 \| 8\.41 + 0.2(578.42 - 570.02 - 8.41) = 8.41 \| \| 11 \| \| 577\.40 + 8.41 = 585.81 \| \| \| The forecast for period 11 is 585.81. page 14 of 24 Pennsylvania State University �2007 [previous](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_13.html) \\| [contents](https://courses.worldcampus.psu.edu/welcome/mangt515/toc.html) \\| [next](https://courses.worldcampus.psu.edu/welcome/mangt515/lesson02_15.html)
Readable Markdown	### Example of Trend-Adjusted Exponential Smoothing For the data given below, generate a forecast for period 11 through 13 using trend-adjusted exponential smoothing. Use ![alpha](https://courses.worldcampus.psu.edu/images/all_lessons/mangt515_alpha.gif) = 0.4 and ![beta](https://courses.worldcampus.psu.edu/images/all_lessons/mangt515_beta1.gif) = 0.3 \| \| \| \| \| \| \| \| \| \| \| \| \|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\| \| Period \| 1 \| 2 \| 3 \| 4 \| 5 \| 6 \| 7 \| 8 \| 9 \| 10 \| \| Data values \| 500 \| 524 \| 520 \| 528 \| 540 \| 542 \| 558 \| 550 \| 570 \| 575 \| Solution: To use trend adjusted exponential smoothing, we first need an initial estimate of the trend. This initial estimate can be obtained by calculating the net change from the three changes in the data that occurred through the first four periods. - Initial Trend Estimate = (528 - 500)/3 = 28/3 = 9.33 Using this initial trend estimate and the actual data value for period 4, we compute an initial forecast for period 5. - Initial Forecast for period 5 = 528 + 9.33 = 537.33. The forecasts and the associated calculations are shown in the table below. \| Period \| Actual \| St-1 \+ Tt-1 \= TAFt \| TAFt \+ 0.3(At \-TAFt ) = St \| Tt-1 \+ 0.2(TAFt \-TAFt-1 \- Tt-1 ) = Tt \| \|---\|---\|---\|---\|---\| \| 5 \| 540 \| 528 + 9.33 = 537.33 \| 537\.33 + 0.3(540 - 537.33) = 538.13 \| 9\.33 \| \| 6 \| 542 \| 538\.13 + 9.33 = 547.46 \| 547\.46 + 0.3(542 - 547.46) = 545.82 \| 9\.33 + 0.2(547.46 - 537.33 - 9.33) = 9.49 \| \| 7 \| 558 \| 545\.82 + 9.49 = 555.31 \| 555\.31 + 0.3(558 - 555.31) = 556.12 \| 9\.49 + 0.2(555.31 - 547.46 - 9.49) = 9.16 \| \| 8 \| 550 \| 556\.12 + 9.16 = 565.28 \| 565\.28 + 0.3(550 - 565.28) = 560.70 \| 9\.16 + 0.2(565.28 - 555.31 - 9.16) = 9.32 \| \| 9 \| 570 \| 560\.70 + 9.32 = 570.02 \| 570\.02 + 0.3(570 - 570.02) = 570.01 \| 9\.32 + 0.2(570.02 - 565.28 - 9.32) = 8.41 \| \| 10 \| 575 \| 570\.01 + 8.41 = 578.42 \| 578\.42 + 0.3(575 - 578.42) = 577.40 \| 8\.41 + 0.2(578.42 - 570.02 - 8.41) = 8.41 \| \| 11 \| \| 577\.40 + 8.41 = 585.81 \| \| \| The forecast for period 11 is 585.81.
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