Multiple Regression Equation

epiphyte · #1 (**permalink**) 12-14-2007, 05:32 PM

Hi Everybody,

Quite often I'll come across a species description that includes county of origin and elevation but neglects to mention minimum temperatures...which is a fairly significant factor in deciding which orchids to try to grow outdoors in temperate areas.

It's been around 10 years since I took a statistics class and math was never my strong point but I googled around and found out how to create a multiple regression equation using excel that would predict the lowest average minimum temperature of a species based on elevation and latitude.

For example, let's say that there was an epiphytic orchid native to my hometown of Glendale, CA (I wish) and I wanted to figure out the lowest average minimum temperature that it was subjected to... I would find out the latitude and elevation...

Lat = 34
Elev = 256

and input it into the following equation...

Min = 77.35541724 - 0.838402676(Lat) - 0.003051964(Elev)

Min = 77.35541724 - 0.838402676(34) - 0.003051964(256)

Min = 77.35541724 - 28.505690983999997 - 0.781302784

Min = 48.068423472

So basically the lowest average minimum temperature for my local orchid would be 48 degrees. The website I used to figure out my Lat/Elev and double check my lowest minimum was WeatherReports.com. To create the equation I used the climate data for 394 northern hemisphere occurring epiphytic orchid species.

Out of the 394 entries one prediction was off by was 22 degrees. But the average degree difference between the predicted and actual was just under 3 degrees. Please feel free to post how accurate it was for your location. If there are any math people out there who would be interested in double checking my calculations let me know and I'll e-mail you the Min/Lat/Elev data.

Obviously, there are numerous factors in selecting orchids that are suitable for growing outdoors year around in your area. The above equation should most definitely not be used as the sole determining factor. Well... unless you have numerous duplicates and won't cry yourself to sleep at night if you sacrifice one in the name of orchid research. If that's the case then message me and I'll give you my address so you can mail me one of your duplicates.

zero742 · #2 (**permalink**) 12-14-2007, 06:42 PM

Excellent!!! Finally some math on here(I'm a physics/mathematics major)! That is pretty interesting though. Good resource.

pikevi · #3 (**permalink**) 12-14-2007, 07:32 PM

That is very interesting, epiphyte.

I tried for our region and it came to about 41F.

Now the task of checking and comparing the various local species to see if they conform.

Thanks.

Hummer344 · #4 (**permalink**) 12-15-2007, 12:55 AM

I understand how the formula works, but where did you get the constants?
For exp: 77.35541------

snowballsarebad · #5 (**permalink**) 12-15-2007, 01:43 PM

Looks cool. However, I'm not sure those would be the best predictors. Latitude might not be specific enough for the equation; you might need to factor in something about maritime climate (which might have considerable overlap with elevation, but...there is a difference). I'm just thinking about islands and such, which despite having similar elevations and latitudes to other places in the world, have very different climates because the ocean keeps them more constant. A similar effect occurs in the Great Lakes area (Michigan, Ohio, Wisconsin, Minnesota, New York, Ontario, etc. Within several miles of the shores of the Great Lakes, you get less extreme weather. Warmer in winter, cooler in summer than areas that are farther from the lakes. This doesn't have much to do with elevation, largely because these areas are mostly flat, and the lakes are all quite a bit above sea level.
Anyhow, I know you said there were many other variables in the equation. This might just be one of them. I wonder if there might be a way to factor it in.
Oh, and I just finished learning some basics about multiple and hierarchical regression this semester...and will be spending an entire semester on it starting in January...and possible another semester after that. I am impressed with your equation.

Do you have any R-squares for it? R-square adjusted? p-values for the model as a whole? I'm not sure if Excel would give you those, but SPSS certainly would.

epiphyte · #6 (**permalink**) 12-16-2007, 12:58 AM

Hummer344:

The constants were supplied by the Excel data analysis feature after I supplied the raw data...

Coefficients:
Intercept 77.35541724
LAT -0.838402676
ELEVATION -0.003051964

Then I just plugged them into this formula

Y=a + b1X1 + b2X2 + b3X3 ...

Y = dependent variable
a = intercept
b1 = coefficient for X1
X1 = first independent variable
b2 = coefficient for X2
X2 = second independent variable
and so forth

so basically, Excel came up with the constants and how Excel derived those constants from the raw data... I have no idea. But perhaps after this semester Snowballsarebad will be able to tell us.

Snowballsarebad:

Maritime influence is definitely an important factor but the problem is that I don't have any "distance from major body of water" data for the orchids that were used. I can send you the list of 394 orchids along with their lat/longs and perhaps you can trick your professor into letting you do a multiple regression project on them in order to justify researching the distances. Shouldn't be too hard using google earth... just tedious. Although it is kind of fun flying and zooming around the world.

In any case, latitude and longitude are pretty decent predictors of temperature. Excel does happen to provide the R squares along with the p-values. I know that the closer the R values are to 1... the more accurate the factors are.

Multiple R 0.911125703
R Square 0.830150047
Adjusted R Square 0.82928125
Standard Error 3.758026804
Observations 394

So, .80 isn't too shabby but if we included maritime, as you mentioned, it would probably get closer to 1.

Here are the P-values... no idea what they mean

Intercept: 0
LAT: 4.7503E-101
ELEVATION: 2.1239E-120

pikevi · #7 (**permalink**) 12-16-2007, 08:10 AM

Somehow I get the feeling I will have to go back to school

.

Thanks epiphyte.

cupcake · #8 (**permalink**) 12-16-2007, 10:33 AM

Whooooooah! That's gone way over my head!

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