In addition to my passion for the outdoors I also enjoy using my hobbyist-level statistics background to build models to predict deer movements. I've done this kind of modeling for my family and friends and they've had a pretty good success rate so I thought it might be worth sharing. As animals are often impacted by external factors, using weather data alone can yield up to 90% accurate forecasts. Like in any forecast there’s always some error involved, but hopefully this will either help you or at the least, be an interesting read for the upcoming season. There is a lot of useful software out there, but I used excel as it’s one of the most widely available. Throughout this tutorial I used Excel’s analysis toolpack. So before you get started, go ahead and download the toolpack. This toolpack should already come with your version of excel, but if it doesn’t, you’ll likely be prompted to download it. If you are using a different program altogether, I suggest finding an add-in that has the word step-wise regression in it. In this tutorial you’re going to be working with a statistical method called step-wise regression. Regressions allow you to put together a formula, in this case, one that uses weather forecasts to predict your deer activity. To get my deer activity I used Trailcam Data to log my images and get weather data, but you can also manually review and tag your images yourself as well. The weather data includes all the variables you think might impact your deer activity, including temperature, barometric pressure, wind speed, precipitation, dew point, cloud coverage, and anything else you can think of. I'm using a very small sample of data just for the purposes of this tutorial so the model based on these numbers should not be used! The next step to do is to scroll up to the Data tab in the ribbon and click on Data Analysis. This will open a text box with several options. All that’s important to focus on is the item called Regression. Go ahead and click on regression and select ok. In the next step you’ll be prompted with a text box. The ‘Input Y Range’ will be your deer activity. This will be the deer you have tagged in your images. To select this data, simply click on the up arrow next to the text box and select the column with the label included. The ‘Input X Range’ will include all your weather information. The X Range serves as all your X variables you think might impact your deer activity. If there are any other variables you think might impact deer activity outside of weather, feel free to incorporate those as well. Go ahead and select the columns like the way you did with the ‘Input Y Range’. Check the ‘Labels’ checkbox. As for the confidence level, all it really tells you is how accurate you want your model to be. There are a few things to consider, for example, how much data do you have? In my example I used 12 days’ worth of data. Within those 12 days I used a small sample of 62 images grabbed from cameras that were placed on a small piece of land. So to think that I have enough data to forecast all deer activity with 100% accuracy with all the deer in the nearby area may be a bit too aggressive. And the higher you adjust the confidence level, the less likely you’ll be able to build a model that really gives you value. So in this case I don’t recommend going over a 90% confidence level. What that tells me is I’m giving myself a 10% chance of being wrong. The 10% number is important to remember, more specifically as 0.1 for the next steps. This 0.1 number is also referred to as your alpha. I prefer to output my information near my data, so I usually check the ‘Output Range’ radio button and place it near my data. Then press ‘Ok’. The regression output will look like the one in the image above. I highlighted all the items that won’t be important for this exercise in red to make this an easier process. As you can see there are just 5 numbers that we’ll be focusing on for the entire tutorial. ‘R Square’: Determines how useful the model is below to describe the changes in deer activity. ‘Standard Error’: The amount of error you can expect from the given output using the model. ‘Observations’: In this case, the number of days that are being analyzed. ‘Coefficients’: This will be reviewed in more depth later, but these are the “multiplier” numbers used to multiply by your weather forecast. ‘P-Value’: This is the most critical for the first steps in the exercise. The P-value determines whether the variable is useful. The values to focus on will be the P-Values. When setting your confidence interval you might remember setting it at 90%, giving a 10% or 0.1 level of error. The variables should be below a P-Value of 0.1. In the case above, none of the values are below 0.1. In fact, there are a few #NUM! values. The first step will be to remove all those variables that have the #NUM! values. To remove the variables with the #NUM! values, simply delete the columns with that data. In the example above, that will be the Average Temperature, and Visibility. If you don't have #NUM! values, skip this step and go to the next. Once you’ve removed your variables go ahead and rerun the regression, repeating the steps above. This time around my P-Values have all dropped, which should happen. Once you have the new P-Values, check to see if any are above 0.1, and see which one is the highest number. In the example above, that will be Humidity. For the next step, delete your column of data with the highest P-Value (i.e. Humidity) and rerun the regression model. Keep repeating these steps one variable at a time until all P-Values are below 0.1. You’ll notice that your P-Values will begin to drop as you start removing variables. Once you’ve found the set of variables that all have P-Values below 0.1, you will have your model ready to use! In the example above my R-Square is 0.905, which means that my model can explain 90.5% of the changes in deer activity with the weather variables. To put the model together, copy the numbers in the Coefficients column and paste them below, in this case with the label ‘m-values’. And that should be it! Now you can take your weather forecasts, paste them below the ‘m-values’ row, which I labeled as ‘x-values’. Then, multiply the forecasts with the above ‘m-values’ and add them all together. The formula above in excel should look something like ‘=-57759.4 + (1.173*88.32) + (-2.82*2.24) + (306.34*0.0081) + (56.76*1016.07)’ I used the previous weather information to compare my deer activity prediction with the actual deer activity. In this case I got 15.79, which is close to the actual 15, and that should be acceptable as my error was +/- 1.5 (just below the ‘Adjusted R-Square’ value). I went a step further to show how my forecasted deer activity compared to my actual deer activity. As you can see, the numbers are pretty close. A note to keep in mind, if your weather forecast numbers are outside the range that you had when putting the model together (ie. your forecasted temperature is 70 degrees, but your model only had temperature values between 75 and 80) then you won’t get as accurate of a deer movement prediction. I’ve posted a video version of this process at Trailcam Data's blog: https://bit.ly/2vt45U4 Hope this was an interesting and useful read! Feel free to reply below and I will do my best to help any way I can.
