<?xml version="1.0" encoding="utf-8"?>
<ManualTopic ID="/baanerp/cp/onlinemanual/000111" xml:lang="en">
   <Header>
      <Title>Forecast method: polynomial regression</Title>
      <Keyword type="header" order="d1e190495">
         <Level1>Forecast method: polynomial regression</Level1>
      </Keyword>
      <Keyword type="header" order="d1e190498">
         <Level1>Polynomial regression</Level1>
      </Keyword>
   </Header>
   <GeneralSection>
      <Paragraph>LN calculates the
      demand forecast according to the <GUIRef href="/baanerp/cp/domains/rpd.fcmd#pr" role="option">Polynomial Regression</GUIRef> forecast method on the basis of an n'th degree polynom,
      which matches the historic demand data.</Paragraph>
      <List>
         <ListIntro>The relevant parameters for this forecast method are:</ListIntro>
         <ListItem> 
            <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.dgpr" role="manual">Degree for Polynomial Regression</GUIRef>
         </ListItem>
         <ListItem> 
            <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.tosi" role="manual">Type of Seasonal Influence</GUIRef>
         </ListItem>
         <ListItem> 
            <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.sctm" role="manual">Seasonal Cycle Time</GUIRef>
         </ListItem>
         <ListItem> 
            <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.aufp" role="manual">Automatic Update of Forecast Parameters</GUIRef>
         </ListItem>
      </List>
      <Paragraph>You can maintain these
      parameters in the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000" role="session">Plan Items - Forecast Settings (cpdsp1110m000)</GUIRef> session.</Paragraph>
      <Paragraph>The polynom's degree is
      indicated by the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.dgpr" role="manual">Degree for Polynomial Regression</GUIRef> field. If the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.aufp" role="manual">Automatic Update of Forecast Parameters</GUIRef> check box is selected, LN determines the polynom's
      optimum degree.</Paragraph>
      <GeneralSection>
         <SectionTitle>Trend-adjusted average demand</SectionTitle>
         <Paragraph>First, the historical
        demand figures are adjusted with the trend-adjusted average demand for the
        relevant period.</Paragraph>
         <Paragraph>Without seasonal
        influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>TD(t) =	 AV</Paragraph>
         </Formula>
         <Paragraph>With a linear trend
        influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>TD(t) = CS + TF * t</Paragraph>
         </Formula>
         <Paragraph>With a progressive trend influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>TD(t) = BS * TF ^ (t-1)DM(t) = AD(t) - TD(t)</Paragraph>
         </Formula>
         <Paragraph>Where:</Paragraph>
         <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
            <TBODY noTR="7">
               <TR no="1" isLast="false">
                  <TD rowspan="1" colspan="1">DM(t)</TD>
                  <TD rowspan="1" colspan="1">trend-adjusted average
              demand for period t</TD>
               </TR>
               <TR no="2" isLast="false">
                  <TD rowspan="1" colspan="1">TD(t)</TD>
                  <TD rowspan="1" colspan="1">trend-based demand for
              period t</TD>
               </TR>
               <TR no="3" isLast="false">
                  <TD rowspan="1" colspan="1">AD(t)</TD>
                  <TD rowspan="1" colspan="1">actual demand for period
              t</TD>
               </TR>
               <TR no="4" isLast="false">
                  <TD rowspan="1" colspan="1">AV</TD>
                  <TD rowspan="1" colspan="1">average demand
              (*)</TD>
               </TR>
               <TR no="5" isLast="false">
                  <TD rowspan="1" colspan="1">CS</TD>
                  <TD rowspan="1" colspan="1">constant
              demand</TD>
               </TR>
               <TR no="6" isLast="false">
                  <TD rowspan="1" colspan="1">BS</TD>
                  <TD rowspan="1" colspan="1">estimated demand for period
              1</TD>
               </TR>
               <TR no="7" isLast="true">
                  <TD rowspan="1" colspan="1">TF</TD>
                  <TD rowspan="1" colspan="1">trend factor</TD>
               </TR>
            </TBODY>
         </TABLE>
         <Paragraph>(*) The average demand
        is the sum of the historical demand figures by period, divided by the number of
        periods with demand history.</Paragraph>
      </GeneralSection>
      <GeneralSection>
         <SectionTitle>Coefficients of the polynom</SectionTitle>
         <Paragraph>LN calculates the
        coefficients of the polynom with the polynomial regression method. See the Related topics for more information about polynomial regression.</Paragraph>
      </GeneralSection>
      <GeneralSection>
         <SectionTitle>Demand forecast</SectionTitle>
         <Paragraph>LN calculates the
        demand for each forecast period based on the trend-adjusted average demand for
        the period in question, increased with the average noise in the past.</Paragraph>
      </GeneralSection>
      <GeneralSection>
         <SectionTitle>Noise</SectionTitle>
         <Paragraph>The noise is the
        fluctuation of the demand data compared to the trend that has been determined.
        The average noise is determined for each forecast period based on the history
        periods which are a whole number of seasonal cycles ago.</Paragraph>
      </GeneralSection>
      <Note>
         <SectionTitle>Note</SectionTitle>
         <Paragraph>If the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.tosi" role="manual">Type of Seasonal Influence</GUIRef> field is <GUIRef href="/baanerp/cp/domains/rpd.tosi#not.in.use" role="option">Not Applicable</GUIRef>, LN assumes a fictitious seasonal cycle with a season
        length of up to a quarter of the number of periods with historical demand.</Paragraph>
      </Note>
      <ExampleSection>
         <SectionTitle>Example</SectionTitle>
         <Paragraph>Figure 1 shows the
        history demand data of two seasonal cycles, which consist of 8 forecast
        periods. Period 9 is the current period.</Paragraph>
         <Figure space-and-orientation="indented-estimated">
            <HTML:IMG xmlns:HTML="http://www.w3.org/TR/REC-html40" height="252" width="432"
                      SRC="../images/nt_graph_000111a.gif"
                      alt="[...]"/>
            <FigCaption>Figure 1</FigCaption>
            <FigLegend>
               <LegendEntry>
                  <Symbol>SCT</Symbol>
                  <Desc>seasonal cycle time</Desc>
               </LegendEntry>
            </FigLegend>
         </Figure>
         <Paragraph>Figure 2 shows the polynom that is determined with polynomial
        regression.</Paragraph>
         <Figure space-and-orientation="indented-estimated">
            <HTML:IMG xmlns:HTML="http://www.w3.org/TR/REC-html40" height="252" width="432"
                      SRC="../images/nt_graph_000111b.gif"
                      alt="[...]"/>
            <FigCaption>Figure 2</FigCaption>
         </Figure>
         <Paragraph>For each history period, the demand based on the polynom is
        compared to the trend of the demand. A linear trend is assumed to be present,
        characterized by the following formula:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>TD(t) = CS + TF * t</Paragraph>
            <FigLegend>
               <LegendEntry>
                  <Symbol>TD (t)</Symbol>
                  <Desc>trend based demand for period t</Desc>
               </LegendEntry>
               <LegendEntry>
                  <Symbol>CS</Symbol>
                  <Desc>constant demand (= 54)</Desc>
               </LegendEntry>
               <LegendEntry>
                  <Symbol>TF</Symbol>
                  <Desc>trend factor (= 2)</Desc>
               </LegendEntry>
            </FigLegend>
         </Formula>
         <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
            <TBODY noTR="9">
               <TR no="1" isLast="false">
                  <TD rowspan="1" colspan="1">Period</TD>
                  <TD rowspan="1" colspan="1">Polynom</TD>
                  <TD rowspan="1" colspan="1">Trend</TD>
                  <TD rowspan="1" colspan="1">Noise</TD>
               </TR>
               <TR no="2" isLast="false">
                  <TD rowspan="1" colspan="1">1</TD>
                  <TD rowspan="1" colspan="1">45</TD>
                  <TD rowspan="1" colspan="1">56</TD>
                  <TD rowspan="1" colspan="1">-11</TD>
               </TR>
               <TR no="3" isLast="false">
                  <TD rowspan="1" colspan="1">2</TD>
                  <TD rowspan="1" colspan="1">53</TD>
                  <TD rowspan="1" colspan="1">58</TD>
                  <TD rowspan="1" colspan="1">-5</TD>
               </TR>
               <TR no="4" isLast="false">
                  <TD rowspan="1" colspan="1">3</TD>
                  <TD rowspan="1" colspan="1">76</TD>
                  <TD rowspan="1" colspan="1">60</TD>
                  <TD rowspan="1" colspan="1">+16</TD>
               </TR>
               <TR no="5" isLast="false">
                  <TD rowspan="1" colspan="1">4</TD>
                  <TD rowspan="1" colspan="1">70</TD>
                  <TD rowspan="1" colspan="1">62</TD>
                  <TD rowspan="1" colspan="1">+8</TD>
               </TR>
               <TR no="6" isLast="false">
                  <TD rowspan="1" colspan="1">5</TD>
                  <TD rowspan="1" colspan="1">49</TD>
                  <TD rowspan="1" colspan="1">64</TD>
                  <TD rowspan="1" colspan="1">-15</TD>
               </TR>
               <TR no="7" isLast="false">
                  <TD rowspan="1" colspan="1">6</TD>
                  <TD rowspan="1" colspan="1">55</TD>
                  <TD rowspan="1" colspan="1">66</TD>
                  <TD rowspan="1" colspan="1">-11</TD>
               </TR>
               <TR no="8" isLast="false">
                  <TD rowspan="1" colspan="1">7</TD>
                  <TD rowspan="1" colspan="1">78</TD>
                  <TD rowspan="1" colspan="1">68</TD>
                  <TD rowspan="1" colspan="1">+10</TD>
               </TR>
               <TR no="9" isLast="true">
                  <TD rowspan="1" colspan="1">8</TD>
                  <TD rowspan="1" colspan="1">70</TD>
                  <TD rowspan="1" colspan="1">70</TD>
                  <TD rowspan="1" colspan="1">+0</TD>
               </TR>
            </TBODY>
         </TABLE>
         <Paragraph>The average noise based on these differences is added to the
        trend-adjusted demand. For example, the average noise for forecast period 9 is
        the average of the noise of periods 1 and 5.</Paragraph>
         <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
            <TBODY noTR="7">
               <TR no="1" isLast="false">
                  <TD rowspan="1" colspan="1">Forecast period</TD>
                  <TD rowspan="1" colspan="1">Trend</TD>
                  <TD rowspan="1" colspan="1">Average
              noise</TD>
                  <TD rowspan="1" colspan="1">Based on periods</TD>
                  <TD rowspan="1" colspan="1">Forecast
              demand</TD>
               </TR>
               <TR no="2" isLast="false">
                  <TD rowspan="1" colspan="1">9</TD>
                  <TD rowspan="1" colspan="1">72</TD>
                  <TD rowspan="1" colspan="1">-13</TD>
                  <TD rowspan="1" colspan="1">1,5</TD>
                  <TD rowspan="1" colspan="1">59</TD>
               </TR>
               <TR no="3" isLast="false">
                  <TD rowspan="1" colspan="1">10</TD>
                  <TD rowspan="1" colspan="1">74</TD>
                  <TD rowspan="1" colspan="1">-8</TD>
                  <TD rowspan="1" colspan="1">2,6</TD>
                  <TD rowspan="1" colspan="1">66</TD>
               </TR>
               <TR no="4" isLast="false">
                  <TD rowspan="1" colspan="1">11</TD>
                  <TD rowspan="1" colspan="1">76</TD>
                  <TD rowspan="1" colspan="1">+13</TD>
                  <TD rowspan="1" colspan="1">3,7</TD>
                  <TD rowspan="1" colspan="1">89</TD>
               </TR>
               <TR no="5" isLast="false">
                  <TD rowspan="1" colspan="1">12</TD>
                  <TD rowspan="1" colspan="1">78</TD>
                  <TD rowspan="1" colspan="1">+4</TD>
                  <TD rowspan="1" colspan="1">4,8</TD>
                  <TD rowspan="1" colspan="1">82</TD>
               </TR>
               <TR no="6" isLast="false">
                  <TD rowspan="1" colspan="1">13</TD>
                  <TD rowspan="1" colspan="1">80</TD>
                  <TD rowspan="1" colspan="1">-13</TD>
                  <TD rowspan="1" colspan="1">1,4</TD>
                  <TD rowspan="1" colspan="1">67</TD>
               </TR>
               <TR no="7" isLast="true">
                  <TD rowspan="1" colspan="1">14</TD>
                  <TD rowspan="1" colspan="1">82</TD>
                  <TD rowspan="1" colspan="1">-7</TD>
                  <TD rowspan="1" colspan="1">2,6</TD>
                  <TD rowspan="1" colspan="1">75</TD>
               </TR>
            </TBODY>
         </TABLE>
         <Paragraph>The result is shown in Figure 3.</Paragraph>
         <Figure space-and-orientation="indented-estimated">
            <HTML:IMG xmlns:HTML="http://www.w3.org/TR/REC-html40" height="252" width="432"
                      SRC="../images/nt_graph_000111c.gif"
                      alt="[...]"/>
            <FigCaption>Figure 3</FigCaption>
         </Figure>
      </ExampleSection>
   </GeneralSection>
   <RelatedTopics>
      <SectionTitle>Related topics</SectionTitle>
      <RelTopic>
         <Link href="/baanerp/cp/onlinemanual/000079" role="manual">Algorithm for demand forecasting</Link>
      </RelTopic>
      <RelTopic>
         <Link href="/baanerp/cp/onlinemanual/000321" role="manual">Forecasting methods</Link>
      </RelTopic>
      <RelTopic>
         <Link href="/baanerp/cp/onlinemanual/000108" role="manual">Principle of polynomial regression</Link>
      </RelTopic>
   </RelatedTopics>
</ManualTopic>