Try to learn something about everything, and everything about somethingThomas Huxley “Darwin's bulldog” (1824-1895)

Trace:

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

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
public:calculator:guides:dm15l_curve_fit [01/02/26 22:05 GMT] – [Background] johnpublic:calculator:guides:dm15l_curve_fit [12/02/26 21:01 GMT] (current) – [DM15L : Non-linear Curve Fit] john
Line 2: Line 2:
  
  
-====== DM15L : Non-linear Curve Fit ======+====== DM15L Non-linear Curve Fit ======
  
 ** Using DM15L/HP15C built-in L.R function to fit non-linear curves ** ** Using DM15L/HP15C built-in L.R function to fit non-linear curves **
Line 10: Line 10:
 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 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 modification.+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>'' | 
  
  
Line 31: Line 61:
 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
Line 39: Line 69:
 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|
  
  
Line 99: Line 130:
 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 ====
  
  
Line 112: Line 143:
 ''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>
Line 165: Line 197:
  
  
-=== Method ===+==== Mechanism ====
  
 Accumulate using  Accumulate using 
Line 180: Line 212:
 ''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>

Navigation