範例：對數遞歸

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範例：對數遞歸

logfit

使用 logfit 函數擬合數據與下列對數方程式：

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            <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">ln</id>
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1. 定義以下矩陣。

按一下以複製此運算式

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        <real>3</real>
        <real>4</real>
        <real>5</real>
        <real>6</real>
        <real>7</real>
        <real>8</real>
        <real>9</real>
        <real>10</real>
        <real>11</real>
        <real>12</real>
        <real>13</real>
        <real>14</real>
        <real>15</real>
        <real>16</real>
        <real>17</real>
        <real>18</real>
        <real>19</real>
        <real>20</real>
        <real>21</real>
        <real>22</real>
        <real>23</real>
        <real>24</real>
        <real>25</real>
        <real>26</real>
        <real>27</real>
        <real>28</real>
        <real>29</real>
        <real>30</real>
        <real>31</real>
        <real>4.181</real>
        <real>4.665</real>
        <real>5.296</real>
        <real>5.365</real>
        <real>5.448</real>
        <real>5.744</real>
        <real>5.653</real>
        <real>5.844</real>
        <real>6.362</real>
        <real>6.38</real>
        <real>6.311</real>
        <real>6.457</real>
        <real>6.479</real>
        <real>6.59</real>
        <real>6.74</real>
        <real>6.58</real>
        <real>6.852</real>
        <real>6.531</real>
        <real>6.682</real>
        <real>7.013</real>
        <real>6.82</real>
        <real>6.647</real>
        <real>6.951</real>
        <real>7.121</real>
        <real>7.143</real>
        <real>6.914</real>
        <real>6.941</real>
        <real>7.226</real>
        <real>6.898</real>
        <real>7.392</real>
        <real>6.938</real>
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2. 定義估值的向量。

函數 ln 僅定義供正數使用。第二個參數會偏移 x 數據，所以可計算 ln。若 x 數據是負值，第二個估值即應為正值，且大到足以將 x 值移至正軸。

在某些情況下，必須調整估值，以取得可能的最佳擬合。第一個值應概述數據的高度及符號，第二個應反映水平位移，第三個則是垂直位移。您可先繪製數據，以決定估值。

3. 使用 logfit 函數求解對數擬合的參數。

第二個參數非常小。函數 lnfit 是很好的 logfit 替代品。

4. 繪製數據與對數擬合。

按一下以複製此運算式

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擬合幾近於完美，如相關係數所證實：

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              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">β</id>
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          </apply>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">vy</id>
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      <unitOverride>
        <placeholder />
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      <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
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lnfit

使用 lnfit 函數擬合數據與下列對數方程式：

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      <apply>
        <plus />
        <apply>
          <mult />
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">a</id>
          <apply>
            <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">ln</id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
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        </apply>
        <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">b</id>
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    </define>
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1. 呼叫 lnfit 求解參數 a 與 b。

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2. 繪製數據與擬合函數。

按一下以複製此運算式

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          <axisLabel />
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3. 計算相關係數。

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此非常接近以 logfit 函數取得的相關性。

相關主題

對數遞歸

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