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public:calculator:guides:dm15l_curve_fit [01/02/26 22:09 GMT] johnpublic:calculator:guides:dm15l_curve_fit [01/02/26 22:26 GMT] (current) – [Method for Power] john
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 The different curves require different treatment of the data to linearize, and the resulting coefficients may require treatment too. The different curves require different treatment of the data to linearize, and the resulting coefficients may require treatment too.
  
-===== Tl;DR =====+===== Tl;dr =====
  
-==== Method for Exponential ====+==== Method for Exponential==== 
 +**y = b.e<sup>ax</sup>** 
 + 
 +'' Ln(y) = a.x + Ln(b) ''
  
 |Enter Accumulation data | '' y<sub>i</sub> <key>'g'</key><key>'Ln'</key> x<sub>i</sub> <key>'∑+'</key>''| |Enter Accumulation data | '' y<sub>i</sub> <key>'g'</key><key>'Ln'</key> x<sub>i</sub> <key>'∑+'</key>''|
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 ==== Method for Logarithmic ==== ==== Method for Logarithmic ====
 +**y=a.ln(x)+b**
 +
 +''y = a.Ln(x) + b ''
  
 |Enter Accumulation data | '' y<sub>i</sub> <key>Enter</key> x<sub>i</sub> <key>'g'</key><key>Ln</key><key>'∑+'</key>''| |Enter Accumulation data | '' y<sub>i</sub> <key>Enter</key> x<sub>i</sub> <key>'g'</key><key>Ln</key><key>'∑+'</key>''|
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 ==== Method for Power ==== ==== Method for Power ====
 +**y=b.x<sup>a</sup>**
 +
 +'' Ln(y) = a.Ln(x) + Ln(b) ''
  
 |Enter Accumulation data |'' y<sub>i</sub> <key>'g'</key><key>Ln</key> x<sub>i</sub> <key>'g'</key><key>Ln</key><key>'∑+'</key>''| |Enter Accumulation data |'' y<sub>i</sub> <key>'g'</key><key>Ln</key> x<sub>i</sub> <key>'g'</key><key>Ln</key><key>'∑+'</key>''|
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 Once the L.R. has run you can find estimates of ''ŷ''  by running the <key>'f'</key><key>'ŷ.r'</key> to get the estimate of ''Ln(y)'' and then finding its antilog  with <key>'e'<sup>x</sup></key> Once the L.R. has run you can find estimates of ''ŷ''  by running the <key>'f'</key><key>'ŷ.r'</key> to get the estimate of ''Ln(y)'' and then finding its antilog  with <key>'e'<sup>x</sup></key>
  
-=== Method ===+==== Mechanism ====
  
 To enter the data points you convert the ''y'' data to its ''Ln'' first, then accumulate as normal To enter the data points you convert the ''y'' data to its ''Ln'' first, then accumulate as normal
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 Once all the data has been entered you get the Linear Regression coefficients ''a'' &  ''b'' <key>'f'</key><key>'L.R.'</key> and <key>'e'<sup>x</sup></key> to correct the ''b'' LR coefficient. Once all the data has been entered you get the Linear Regression coefficients ''a'' &  ''b'' <key>'f'</key><key>'L.R.'</key> and <key>'e'<sup>x</sup></key> to correct the ''b'' LR coefficient.
  
-=== Example Data ===+==== Example Data ===
  
-|**x**|0.8|1.1|1.7|2.1| 
 |**y**|2.8|3.6|5.8|8.0| |**y**|2.8|3.6|5.8|8.0|
 +|**x**|0.8|1.1|1.7|2.1|
  
  
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 To estimate ''ŷ'' first find the ''Ln'' of ''x'' then use the <key>'f'</key><key>ŷ.r</key> To estimate ''ŷ'' first find the ''Ln'' of ''x'' then use the <key>'f'</key><key>ŷ.r</key>
  
-=== Method ===+==== Mechanism ====
  
  
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 ''x''<key>'g'</key><key>Ln</key><key>'f'</key><key>ŷ.r</key> ''x''<key>'g'</key><key>Ln</key><key>'f'</key><key>ŷ.r</key>
  
-=== Example Data ===+==== Example Data ====
  
-|**x**|0.8|1.7|2.6|4.9| 
 |**y**|1.5|1.7|1.8|2.1| |**y**|1.5|1.7|1.8|2.1|
 +|**x**|0.8|1.7|2.6|4.9|
 +
  
 <key>'f'</key><key>clear ∑</key> <key>'f'</key><key>clear ∑</key>
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-=== Method ===+==== Mechanism ====
  
 Accumulate using  Accumulate using 
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 ''x<key>'g'</key><key>Ln</key><key>'f'</key><key>ŷ.r</key><key>'e'<sup>x</sup></key>'' ''x<key>'g'</key><key>Ln</key><key>'f'</key><key>ŷ.r</key><key>'e'<sup>x</sup></key>''
  
-=== Example Data ===+==== Example Data ====
  
-|**x**|0.6|1.3|2.4|3.6| 
 |**y**|1.3|2.2|3.3|4.4| |**y**|1.3|2.2|3.3|4.4|
 +|**x**|0.6|1.3|2.4|3.6|
 +
  
 <key>'f'</key><key>clear ∑</key> <key>'f'</key><key>clear ∑</key>

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