函數
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數據分析
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曲線擬合
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範例：正弦曲線遞歸
範例：正弦曲線遞歸
使用
sinfit
函數可執行正弦曲線遞歸。若數據會定期振盪，則適用此函數。
1.
定義數據集。
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<region id="ID0EU2XS" top="211.20000000000005" left="19.200000000000003" height="27.752000000000002" width="86.156666666666666" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="48" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">vx</id> <apply xml:lang="zh_TW"> <matcol xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data</id> <real xml:lang="zh_TW">0</real> </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" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EG3XS" top="230.40000000000003" left="19.200000000000003" height="27.752000000000002" width="85.966666666666669" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="50" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">vy</id> <apply xml:lang="zh_TW"> <matcol xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data</id> <real xml:lang="zh_TW">1</real> </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" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EY3XS" top="307.20000000000005" left="19.200000000000003" height="111.24000000000001" width="162.19333333333333" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="52" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <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="4,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
2.
定義估值的向量。
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在某些情況下，必須調整估值，以取得可能的最佳擬合。第一個值應近似於數據的振幅，第二個值應等於相角位移，而第三個值應等於位移。
3.
呼叫
sinfit
函數求解正弦曲線擬合的參數。
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<region id="ID0E5AYS" top="652.80000000000007" left="19.200000000000003" height="62.800000000000004" width="204.70333333333335" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="58" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">β</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <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" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
參數即為在下列正弦曲線方程式中所求得者：
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4.
繪製數據與正弦曲線擬合。
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<region id="ID0E3DYS" top="844.80000000000018" left="19.200000000000003" height="47.2" width="88.563333333333333" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="64" 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 labels="*" xml:space="preserve" xml:lang="zh_TW">range</id> <id labels="*" xml:space="preserve" xml:lang="zh_TW">i</id> </apply> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id xml:space="preserve" xml:lang="zh_TW">i</id> <real xml:lang="zh_TW">10</real> </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" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EOEYS" top="883.20000000000016" left="0" height="312" width="622" 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 resultRef="66" xml:lang="zh_TW"> <traceStyle color="#FFFF0000" symbol="x" line-weight="1" line-style="None" xml:lang="zh_TW">線條</traceStyle> </trace> <trace resultRef="67" xml:lang="zh_TW"> <traceStyle color="#FF000000" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle> </trace> </traces> <graph-size width="483.6" height="216" xml:lang="zh_TW" /> <axes xml:lang="zh_TW"> <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="50" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="5" legendWidth="92.1466666666667" 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"> <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> </numberFormat> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="68" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">vx</id> </math> <math resultRef="69" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation xml:lang="zh_TW"> <math resultRef="70" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">range</id> </math> <math resultRef="71" 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"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </startValue> <endValue xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </endValue> </xyDomain> </xAxis> <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-10" end="10" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="0" legendWidth="113.52" 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"> <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> </numberFormat> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="76" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">vy</id> </math> <math resultRef="77" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation xml:lang="zh_TW"> <math resultRef="78" xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:space="preserve" xml:lang="zh_TW">f</id> <id xml:space="preserve" xml:lang="zh_TW">range</id> </apply> </math> <math resultRef="79" 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 resultRef="73" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-10</real> </startValue> <endValue xml:lang="zh_TW" resultRef="75"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">10</real> </endValue> </xyDomain> </yAxis> </axes> </xyPlot> </plot> </region>
擬合幾近於完美，如相關係數所證實：
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複製運算式
