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You are here: Home » Public Area » Calculators » Hints & Tips » DM15L : Non-linear Curve Fit

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public:calculator:guides:dm15l_curve_fit [01/02/26 22:00 GMT] – [Logarithmic] johnpublic:calculator:guides:dm15l_curve_fit [01/02/26 22:26 GMT] (current) – [Method for Power] john
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 ===== Background ===== ===== Background =====
  
-The idea is to "pre-distort" the data with a function before adding them to the statistics accumulator.+The idea is that the 3 different non-linear function forms can be expressed as linear expression ''y = m.x + c'' if we manipulate the ''x'' or ''y'' values before adding them to the statistics accumulator.  
 + 
 +The different curves require different treatment of the data to linearize, and the resulting coefficients may require treatment too. 
 + 
 +===== Tl;dr ===== 
 + 
 +==== 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>''| 
 +|Calculate coefficients | ''<key>'f'</key><key>'L.R.'</key><key>'e'<sup>x</sup></key>''| 
 +|Estimate ŷ & r for a new ''x'' | ''x <key>'f'</key><key>'ŷ.r'</key> <key>'e'<sup>x</sup></key>''| 
 + 
 +==== 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>''| 
 +|Calculate coefficients |<key>'f'</key><key>L.R.</key> | 
 +|Estimate ŷ & r for a new ''x'' |''x<key>'g'</key><key>Ln</key> <key>'f'</key><key>ŷ.r</key>'' | 
 + 
 +==== 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>''| 
 +|Calculate coefficients |<key>'f'</key><key>L.R.</key><key>'e'<sup>x</sup></key> | 
 +|Estimate ŷ & r for a new ''x'' |''x <key>'g'</key><key>Ln</key><key>'f'</key><key>ŷ.r</key><key>'e'<sup>x</sup></key>'' |
  
-This "linearizes" the data so that the **L.R.** function finds a linear fit that can be used for ''Y'' estimation. 
  
-Once a Linear Fit has been calculated you manipulate the data / estimation with the appropriate function. 
  
 ===== Exponential ===== ===== Exponential =====
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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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