# Regression Analysis for a Gamma function

1. Jan 19, 2008

### chicopee

[SOLVED] Regression Analysis for a Gamma function

My regression analysis program that I developed in BASICS back in the 1980's applies for half a dozen linear equations some of which are transormed into log forms. I would like to modify my program to include this Gamma function: I(t)=P*(t^s)*(e^(-ft)) which I can transform into this equivalent non- linear log form: Ln I(t)=Ln P + s*Ln t + (-ft); P,s and f are constants; t if for time; I(t) has for units cu.ft/sec or cu.m./sec. Is there any way to take care of the term (-ft). I got 18 data points available for this regression .

I am not looking forward to trial and error to determine the constants P,s and f.

Here is another thought. Since I have 18 data points (flow vs time), can I solve theses constants with matrices using this transformation: Ln I(t)=Ln P + s*Ln t + (-ft) eventho I would have 18 rows and and only 4 columns?

2. Jan 19, 2008

### chicopee

Note, my request is not homework. This is a real situation involving a flooding situation arising from tropical storm Tammy back in 2005.

3. Jan 19, 2008

### EnumaElish

Why not run the regression y(t) = a + b1 x1(t) + b2 x2(t) + error, where y = log I, x1 = log t, x2 = t, and the parameters are a = Log P, b1 = s, b2 = -f?

4. Jan 20, 2008

### chicopee

Yeah, I see what you mean. Instead of one independent variable, I'll two in that transformed equation. Thx.