Real life problem

• Mar 2nd 2009, 11:21 AM
gilgatex
Real life problem
I think this is the right forum; I've been out of high school for 10 years but I can't remember any of this stuff. I have these three data sets, taken from my real life travels:

Ohio:
Number of Counties: 88
Average Size per county: 465.33 square miles
Time to traverse all 88 counties: 84874 seconds

Alabama:
Number of Counties: 67
Average Size per county: 757.48 square miles
Time to traverse all 67 counties: 76482 seconds

Delaware:
Number of Counties: 3
Average Size per county: 651.67
Time to traverse 3 counties: 2700 seconds

I would like to calculate an equation that, if given the number of counties and average size per county of a state, I could calculate how long it would take to traverse all the counties of that state.

Thanks
• Mar 2nd 2009, 11:37 AM
mateoc15
(Wondering)

What is the source of this data? Are all three independent? I thought at first that maybe it was a calculation, like 84874/88 = 465.33 but that's definitely not the case.

There's no linear equation that will map three different variables. If you want to do just two you could do that. Otherwise it gets really complicated I think.
• Mar 2nd 2009, 11:40 AM
gilgatex
Unfortunately I'm looking for the complicated answer, because it's not linear. These are independent data points that I have collected myself.

When I tried to solve the first two linearly (Ohio & Alabama), the answer for Delaware was over 9 hours, so I knew that couldn't be right.
• Mar 2nd 2009, 12:16 PM
mateoc15
Ok, I see now. What you're looking for is non-linear regression (more than 2 variables). I know that Microsoft Excel has some good functions for linear regression (just two variables) but have never used it for more than two.

I would just try a search for "non-linear regression software" or something similar. That may help you identify an equation that might give you a rough idea. I can guarantee you that you won't find a 100% perfect line of fit. I assume you're just looking for something close.

Hope this helps.
• Mar 2nd 2009, 12:18 PM
gilgatex
That helps a lot! I'll look into it, thanks!
• Mar 2nd 2009, 12:24 PM
mateoc15
Regression Tools - Online Nonlinear Regression
Although I've never used this myself here's a free online tool. You really need to understand the basics of linear regression before diving into non-linear. Look for an example of linear regression with Excel and get an idea of what it does, then look into non-linear.

Also, the more data points the better. So if you have info for all 50 states you should do it that way for sure.
• Mar 2nd 2009, 12:32 PM
gilgatex
I have three values for my set, but non-linear regression only takes two?
• Mar 2nd 2009, 12:43 PM
mateoc15
Linear regression - Wikipedia, the free encyclopedia
The very basics of linear regression is that your goal is to plot all of your X/Y points on a graph and then draw a line through the middle that "fits" them. The equation of that line is a guideline for how your data behaves and based on any given value of X you should be able to predict Y with at least some accuracy.

The problem is that visually it's easy to plot X and Y because there are only two dimensions. If you have an X, Y, and Z (as you do) it's hard to map it out on paper.

Check the link above for linear to get the basics, then check out this one:

Nonlinear regression - Wikipedia, the free encyclopedia