onlineregression13:   Multiple linear regression   ⇒   y = f(x1, x2)

Formulas

t1 = n∑yx2 - ∑y∑x2           t2 = n∑x1∑x2 - ∑x1∑x2

t3 = n∑x22 - (∑x2)2           t4 = n∑yx1 - ∑y∑x1

t5 = n∑x1x2 - ∑x1∑x2           t6 = n∑x12 - (∑x1)2

t7 = n∑x22 - (∑x2)2

β1 = (t1*t2 - t3*t4)/(t5*t5 - t6*t7)

β2 = (t4 - β1*t6)/t2

α = (∑y - β1∑x1 - β2∑x2)/n

Reference

Ponce, V. M. 1989. Engineering Hydrology, Principles and Practices. Prentice Hall, page 241-243.
Example
INPUT DATA:

Enter array size n:     

Enter corresponding values of arrays y, x1 and x2 (separate each value with a comma; maximum string length is 300 characters).

y:     

x1:     

x2:     

ECHO OF INPUT:

n =  

y(1) =  .   

x1(1) =  .   

x2(1) =  .   

OUTPUT:

α =            β1 =            β2 =           

            

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