函數
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數據分析
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曲線擬合
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範例：中值-中值遞歸
範例：中值-中值遞歸
使用
medfit
函數計算數據集的「中值-中值」直線擬合。
1.
定義數據集。
<region id="ID0EGS4R" top="96" left="48" height="26.1965" width="138.06" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:lang="zh_TW" label="None">X</id> <apply xml:lang="zh_TW"> <transpose xml:lang="zh_TW" /> <matrix rows="1" cols="7" xml:lang="zh_TW"> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">2</real> <real xml:lang="zh_TW">3</real> <real xml:lang="zh_TW">4</real> <real xml:lang="zh_TW">5</real> <real xml:lang="zh_TW">6</real> <real xml:lang="zh_TW">7</real> </matrix> </apply> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EYS4R" top="120" left="48" height="26.1965" width="167.503333333333" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:lang="zh_TW" label="None">Y</id> <apply xml:lang="zh_TW"> <transpose xml:lang="zh_TW" /> <matrix rows="1" cols="7" xml:lang="zh_TW"> <real xml:lang="zh_TW">4</real> <real xml:lang="zh_TW">7</real> <real xml:lang="zh_TW">10</real> <real xml:lang="zh_TW">13</real> <real xml:lang="zh_TW">16</real> <real xml:lang="zh_TW">19</real> <real xml:lang="zh_TW">70</real> </matrix> </apply> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
最後一個點是離群值：
<region id="ID0EPT4R" top="168" left="48" height="29.6" width="45.78" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <indexer xml:lang="zh_TW" /> <id xml:lang="zh_TW" label="None">Y</id> <real xml:lang="zh_TW">6</real> </apply> <real xml:lang="zh_TW">70</real> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
2.
呼叫
medfit
函數求解「中值-中值」直線擬合的係數。使用這些係數定義「中值-中值」線。
<region id="ID0EJV4R" top="240" left="48" height="41.693" width="111.366666666667" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <matrix rows="2" cols="1" xml:lang="zh_TW"> <id xml:lang="zh_TW" label="None">a</id> <id xml:lang="zh_TW" label="None">b</id> </matrix> <apply xml:lang="zh_TW"> <id xml:lang="zh_TW">medfit</id> <sequence xml:lang="zh_TW"> <id xml:lang="zh_TW">X</id> <id xml:lang="zh_TW">Y</id> </sequence> </apply> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0E2V4R" top="288" left="48" height="21.2" width="99.1" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <function xml:lang="zh_TW"> <id xml:lang="zh_TW" label="None">med</id> <boundVars xml:lang="zh_TW"> <id xml:lang="zh_TW" label="None">x</id> </boundVars> </function> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <id xml:lang="zh_TW">a</id> <apply xml:lang="zh_TW"> <mult xml:lang="zh_TW" /> <id xml:lang="zh_TW">b</id> <id xml:lang="zh_TW">x</id> </apply> </apply> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
3.
呼叫
line
函數求解最小平方線性擬合的係數。使用這些係數定義最佳擬合線。
<region id="ID0EVX4R" top="360" left="48" height="41.693" width="95.72" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <matrix rows="2" cols="1" xml:lang="zh_TW"> <id xml:lang="zh_TW" label="None">c</id> <id xml:lang="zh_TW" label="None">d</id> </matrix> <apply xml:lang="zh_TW"> <id xml:lang="zh_TW">line</id> <sequence xml:lang="zh_TW"> <id xml:lang="zh_TW">X</id> <id xml:lang="zh_TW">Y</id> </sequence> </apply> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EHY4R" top="408" left="48" height="21.2" width="90.98" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <function xml:lang="zh_TW"> <id xml:lang="zh_TW" label="None">lsq</id> <boundVars xml:lang="zh_TW"> <id xml:lang="zh_TW" label="None">x</id> </boundVars> </function> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <id xml:lang="zh_TW">c</id> <apply xml:lang="zh_TW"> <mult xml:lang="zh_TW" /> <id xml:lang="zh_TW">d</id> <id xml:lang="zh_TW">x</id> </apply> </apply> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
4.
繪製數據點與前文定義的兩條線。
<region id="ID0E3Z4R" top="480" left="48" height="312" width="312" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <plot origin-positioning="true" xml:lang="zh_TW"> <xyPlot xml:lang="zh_TW"> <title class="- topic/title " xml:lang="zh_TW" toc="yes" wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" /> <legend xml:lang="zh_TW" /> <traces xml:lang="zh_TW"> <trace xml:lang="zh_TW"> <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="None" xml:lang="zh_TW">線條</traceStyle> </trace> <trace xml:lang="zh_TW" num-of-points="500"> <traceStyle color="#FF000000" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">lines</traceStyle> </trace> <trace xml:lang="zh_TW" num-of-points="500"> <traceStyle color="#FFFF0000" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle> </trace> </traces> <axes xml:lang="zh_TW"> <xAxis rank="1" legend-position="PlotBoundaryBottom" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="6" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">11</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW" /> <numberFormat xml:lang="zh_TW" /> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math xml:lang="zh_TW"> <id xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">X</id> </math> <math xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation xml:lang="zh_TW"> <math xml:lang="zh_TW"> <id xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">x</id> </math> <math xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-10</real> </startValue> <endValue xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">10</real> </endValue> </xyDomain> </xAxis> <yAxis rank="1" legend-position="PlotBoundaryLeft" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="5" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">11</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW" /> <numberFormat xml:lang="zh_TW" /> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math xml:lang="zh_TW"> <id xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">Y</id> </math> <math xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation xml:lang="zh_TW"> <math xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:lang="zh_TW">med</id> <id xml:lang="zh_TW">x</id> </apply> </math> <math xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation xml:lang="zh_TW"> <math xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:lang="zh_TW">lsq</id> <id xml:lang="zh_TW">x</id> </apply> </math> <math xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-120</real> </startValue> <endValue xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">80</real> </endValue> </xyDomain> </yAxis> </axes> </xyPlot> </plot> </region>
線性擬合受離群值的影響比受「中值-中值」擬合的影響來得大。
複製運算式
