Beispiel: Multidfit-Funktion

Funktionen > Statistische Versuchsplanung > Regressionsanalyse > Beispiel: Multidfit-Funktion

Generieren Sie eine Matrix mit Mustern aus den Vektoren X0, X1 und Y für N Punkte.

1. Definieren Sie die Anzahl der Punkte.

2. Generieren Sie die Vektoren X0 und X1.

3. Generieren Sie die Störung für das Signal f(x).

4. Kombinieren Sie die Argumentdaten.

5. Generieren Sie den Y-Datenvektor auf Basis der Werte der f(x)-Funktion und der Störung.

<region id="ID0E2VCX" actualWidth="261.26333333333332" actualHeight="129.4" top="940.80000000000018" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="25">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <indexer />
        <id labels="VARIABLE" xml:space="preserve">Y</id>
        <id labels="*" xml:space="preserve">i</id>
      </apply>
      <eval>
        <apply>
          <plus />
          <apply>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">f</id>
            <apply>
              <transpose />
              <parens>
                <apply>
                  <matrow />
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">X</id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">i</id>
                </apply>
              </parens>
            </apply>
          </apply>
          <apply>
            <indexer />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">disturb</id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">i</id>
          </apply>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
    <resultFormat>
      <matrix size="5,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

6. Definieren Sie die Matrix Data.

7. Definieren Sie die Anpassungsfunktion F(x,u).

8. Suchen Sie die Parameter der Anpassungsfunktion mithilfe der allgemeinen multivariaten Anpassung.

<region id="ID0ET1CX" actualWidth="279.23333333333329" actualHeight="62.800000000000004" top="1478.4000000000003" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="28">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">U</id>
      <eval>
        <apply>
          <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">multidfit</id>
          <sequence>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">X</id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">Y</id>
            <matrix rows="3" cols="1">
              <real>0</real>
              <real>0</real>
              <real>0</real>
            </matrix>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">F</id>
          </sequence>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
  </math>
</region>

Sie haben eine Näherung der Koeffizienten erhalten, die in der ursprünglichen Funktion f(x) verwendet werden.

9. Vergleichen Sie die Data-Matrix und die angenäherte Fläche.

<region id="ID0EM3CX" actualWidth="288" actualHeight="337" top="1747.2000000000003" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="transparent">
    <plot3D>
      <traces>
        <trace3D num-of-points="41" resultRef="34">
          <traceStyle color="#FFED1D2F" symbol="point" line-style="None" line-weight="6" automaticStyle="true">Kurve</traceStyle>
        </trace3D>
        <trace3D num-of-points="41" resultRef="35">
          <traceStyle color="#FF2E3192" automaticStyle="true">surface</traceStyle>
        </trace3D>
      </traces>
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <axes>
        <xAxis start="0" end="1" rank="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <xyDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue resultRef="29">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <endValue resultRef="30">
              <real xmlns="http://schemas.mathsoft.com/math50">1</real>
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis start="0" end="1" rank="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <xyDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue resultRef="31">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <endValue resultRef="32">
              <real xmlns="http://schemas.mathsoft.com/math50">1</real>
            </endValue>
          </xyDomain>
        </yAxis>
        <zAxis start="0" end="3.0000000000000004" rank="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>6</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <zDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue resultRef="33">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <endValue />
          </zDomain>
        </zAxis>
      </axes>
      <plotEquations>
        <plotEquation>
          <math>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">Data</id>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
        <plotEquation>
          <math>
            <apply xmlns="http://schemas.mathsoft.com/math50">
              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">F</id>
              <sequence>
                <matrix rows="2" cols="1">
                  <id xml:space="preserve">x</id>
                  <id xml:space="preserve">y</id>
                </matrix>
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">U</id>
              </sequence>
            </apply>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
      </plotEquations>
      <CameraTransformMatrix Rows="4" Columns="4">
        <Cells>
          <Cell>0.97823637763401561</Cell>
          <Cell>-0.048952317111439492</Cell>
          <Cell>-0.20163645534203492</Cell>
          <Cell>0</Cell>
          <Cell>0.030218490424354278</Cell>
          <Cell>0.995022135742543</Cell>
          <Cell>-0.094962056732260353</Cell>
          <Cell>0</Cell>
          <Cell>0.20528134915269952</Cell>
          <Cell>0.086802189095488161</Cell>
          <Cell>0.97484611486032935</Cell>
          <Cell>0</Cell>
          <Cell>-0.046477228889917177</Cell>
          <Cell>0.0051324295900421132</Cell>
          <Cell>0.03898830210146071</Cell>
          <Cell>1</Cell>
        </Cells>
      </CameraTransformMatrix>
    </plot3D>
  </plot>
</region>

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Allgemeine multivariate Anpassung

Regressionsanalysefunktionen

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