onlineregression12:   One-predictor-variable nonlinear regression   ⇒   y = f(x)

Formulas

y= axb         log(y)= log(a) + b[log(x)]

u= log(x)        v= log(y)         v= log(a) + bu

v= α + βu         log(a)= α        b= β        a= 10α

β= [Σ(uv)-(ΣuΣv)/n]/{Σ(u2)-[(Σu)2/n]}

α= [Σv-(βΣu)]/n        y = 10αxβ

Reference

Ponce, V. M. 1989. Engineering Hydrology, Principles and Practices. Prentice Hall, page 240.
Example
INPUT DATA:

Enter array size n:     

Enter paired values of arrays y and x (separate each value with a comma; maximum string length is 300 characters).

y:     

x:     

ECHO OF INPUT:


Warning: Undefined variable $number in /var/www/html/ponce/onlineregression12.php on line 203
n =  


Warning: Undefined variable $number in /var/www/html/ponce/onlineregression12.php on line 205

Warning: Undefined variable $j in /var/www/html/ponce/onlineregression12.php on line 211

Warning: Undefined variable $yvar in /var/www/html/ponce/onlineregression12.php on line 212

Warning: Trying to access array offset on null in /var/www/html/ponce/onlineregression12.php on line 212
y(1) =  .   


Warning: Undefined variable $number in /var/www/html/ponce/onlineregression12.php on line 215

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Warning: Undefined variable $xvar in /var/www/html/ponce/onlineregression12.php on line 222

Warning: Trying to access array offset on null in /var/www/html/ponce/onlineregression12.php on line 222
x(1) =  .   

OUTPUT:

a =
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Deprecated: substr(): Passing null to parameter #1 ($string) of type string is deprecated in /var/www/html/ponce/onlineregression12.php on line 229
           b =
Warning: Undefined variable $beta in /var/www/html/ponce/onlineregression12.php on line 229

Deprecated: substr(): Passing null to parameter #1 ($string) of type string is deprecated in /var/www/html/ponce/onlineregression12.php on line 229
           y =
Warning: Undefined variable $acoef in /var/www/html/ponce/onlineregression12.php on line 230

Deprecated: substr(): Passing null to parameter #1 ($string) of type string is deprecated in /var/www/html/ponce/onlineregression12.php on line 230
x
Warning: Undefined variable $beta in /var/www/html/ponce/onlineregression12.php on line 230

Deprecated: substr(): Passing null to parameter #1 ($string) of type string is deprecated in /var/www/html/ponce/onlineregression12.php on line 230

            

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Count 

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