# Logarithmic regression Calculator

## Analyzes the data table by logarithmic regression and draws the chart.

 Logarithmic regression: y=A+Bln(x)
 （input by clicking each cell in the table below） data 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 Guidelines for interpreting correlation coefficient r :　　0.7＜|r|≦1        strong correlation　　0.4＜|r|＜0.7     moderate correlation　　0.2＜|r|＜0.4     weak correlation　　0≦|r|＜0.2         no correlation$\normal\ Logarithmic\ regression\vspace{10}\\(1)\ mean:\ \bar{lnx}={\large \frac{{\small \sum}{lnx_i}}{n}},\hspace{10}\bar{y}={\large \frac{{\small \sum}{y_i}}{n}}\\[10](2)\ trend\ line:\ y=A+Blnx,\hspace{10} B={\large\frac{Sxy}{Sxx}},\hspace{10} A=\bar{y}-B\bar{lnx}\\[10]\\(3)\ correlation\ coefficient:\ r=\frac{\normal S_{xy}}{\normal sqrt{S_{xx}}sqrt{S_{yy}}}\\\hspace{20}S_{xx}={\large \frac{{\small \sum}(lnx_i-\bar{lnx})^2}{n}}={\large \frac{{\small \sum} (lnx_i)^2}{n}}-\bar{lnx}^2\\\hspace{20}S_{yy}={\large \frac{{\small \sum}(y_i-\bar{y})^2}{n}}={\large \frac{{\small \sum} y_i^2}{n}}-\bar{y}^2\\\hspace{20}S_{xy}={\large \frac{{\small \sum}(lnx_i-\bar{lnx})(y_i-\bar{y})}{n}}={\large \frac{{\small \sum} lnx_i y_i}{n}}-\bar{lnx}\bar{y}\\$
Logarithmic regression
 [1-4] /4 Disp-Num5103050100200
[1]  2018/11/05 13:33   Male / 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
Obtaining a more exact correlation between pitot tube position in a square air duct and the flow speed for the purpose of finding the volumetric flow rate of air in said duct. I'm a University senior pursuing a B.S. in Mechanical Engineering in a Thermo-Fluid Systems Lab.
[2]  2018/09/21 23:14   Male / 40 years old level / A teacher / A researcher / Very /
Purpose of use
Allocate awards.
[3]  2017/08/22 02:43   Male / 60 years old level or over / An engineer / Very /
Purpose of use
Frequency drift of a quartz crystal oscillator over extended time.
Comment/Request
The Log Regression showed much better correlation to my data than the "built-in" used in excel chart curve-fit utility.

I am told there''s a better way to fit this particular data by using a "sum of log regressions", where 2 independent correlated variables that both follow log function can be modeled. I wold appreciate any feedback, but I''m afraid the details are unknown to me.
[4]  2017/05/16 09:28   Male / Under 20 years old / High-school/ University/ Grad student / Very /
Purpose of use
Education

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