# Do you understand basic system analysis?

**URL:** <http://discourse.iapct.org/t/do-you-understand-basic-system-analysis/3590>\
**Category:** CSG1995\
**Created:** [December 25, 1995, 9:01am UTC](http://discourse.iapct.org/t/do-you-understand-basic-system-analysis/3590 "1995-12-25T09:01:46Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![William\_T\_Powers4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/w/977dab/32.png) [@William\_T\_Powers4](http://discourse.iapct.org/u/William_T_Powers4)\
**Post date:** [December 25, 1995, 9:01am UTC](http://discourse.iapct.org/t/do-you-understand-basic-system-analysis/3590/1 "1995-12-25T09:01:46Z")

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[From Bill Powers (941225.0300 MST)]

All the present or ex EABers:

I don't know why I didn't think of this before, but so it goes: I  
didn't.

Here is a little test for EABers, to see if they understand basic system  
analysis. I've already been claiming that they don't, so there's no  
added loss of face here in failing the test.

Suppose we have a simple fixed-ratio m schedule. We know that the  
apparatus equation is simply

R = B/m,  
where B = mean behavior rate  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;R = mean reinforcement rate  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;m = ratio

We observe that in the steady state with m = 5, R = 16.67 and B = 33.3  
per unit time, and that with m = 10, R = 10 and B = 100. The question  
is, what is the best LINEAR organism-function that will account for  
these observations? The organism function will express B as a function  
of R.

A linear function can be expressed either as a slope-intercept form or  
as a point-slope form. The slope-intercept form is y = ax + b, and the  
point-slope form is y - y0 = c(x - x0). These forms are both the  
equation of a straight line, and the forms are mathematically  
equivalent. Either form can be transformed into the other.

There is only one possible linear form for the organism function, given  
the two sets of observations above. What is it? Use either form for the  
answer.

No trick or complications here; forget about collection time, satiation,  
all the fancy stuff. This is a basic and simple exercise in system  
analysis. There is a unique answer and it can be obtained using high-  
school algebra. What we want is a linear formula expressing behavior  
rate B as a function of reinforcement rate R, nothing more. There is  
only one right answer.

> **···**
>
> -----------------------------------------------------------------------  
> Best,
> 
> Bill P.