Example: Kernel Smoothing

Functions > Data Analysis > Smoothing > Example: Kernel Smoothing

Use the ksmooth function to smooth a data set.

1. Define a random data set.

2. Define the bandwidth for the kernel smoothing.

It is important to select the bandwidth carefully. Too large a bandwidth will wash out details as it averages over the whole data set. Too small a bandwidth may create artificial details in the smoothed data.

3. Call the ksmooth function to perform kernel smoothing on the data set.

4. Plot the data set before and after smoothing.

<region id="ID0EBOBV" top="432" left="24" width="468" height="312" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="true">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="0">
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="None">lines</traceStyle>
        </trace>
        <trace resultRef="1">
          <traceStyle color="#FF000000" symbol="none" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <axes>
        <xAxis legend-position="PlotBoundaryBottom" rank="1">
          <axisLine position="bottom" positionticmark="-1" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xmlns="http://schemas.mathsoft.com/math50">X</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="2">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <endValue resultRef="3">
              <real xmlns="http://schemas.mathsoft.com/math50">5</real>
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis legend-position="PlotBoundaryLeft" rank="1">
          <axisLine position="origin" positionticmark="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xmlns="http://schemas.mathsoft.com/math50">Y</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation>
              <math>
                <id xmlns="http://schemas.mathsoft.com/math50">K</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="4">
              <real xmlns="http://schemas.mathsoft.com/math50">1</real>
            </startValue>
            <endValue resultRef="5">
              <real xmlns="http://schemas.mathsoft.com/math50">8</real>
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>