How to take root mean square error (rmse) in python

What is Root Mean Square Error (RMSE)?

Root Mean Square Error (RMSE) measures how much error there is between two data sets. In other words, it compares a predicted value và an observed or known value. The smaller an RMSE value, the closer predicted & observed values are.

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It’s also known as Root Mean Square Deviation and is one of the most widely used statistics in GIS.

Different than Mean Absolute Error (MAE), we use RMSE in a variety of applications when comparing two data sets.

Here’s an example of how to calculate RMSE in Excel with 10 observed và predicted values. But you can apply this same calculation to any size data phối.

Root Mean Square Error Example

For example, we can compare any predicted value with an actual measurement (observed value).

Predicted valueObserved value

Root mean square error takes the difference for each observed and predicted value.

You can swap the order of subtraction because the next step is to take the square of the difference. This is because the square of a negative value will always be a positive sầu value. But just make sure that you keep the same order throughout.

After that, divide the sum of all values by the number of observations. Finally, we get a RMSE value. Here’s what the RMSE Formula looks like:


How lớn Calculate RMSE in Excel

Here is a quichồng and easy guide to calculate RMSE in Excel. You will need a phối of observed và predicted values:

1. Enter headers

In cell A1, type “observed value” as a header. For cell B1, type “predicted value”. In C2, type “difference”.

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2. Place values in columns

If you have 10 observations, place observed elevation values in A2 khổng lồ A11. In addition, populate predicted values in cells B2 khổng lồ B11 of the spreadsheet

3. Find the difference between observed và predicted values

In column C2, subtract observed value and predicted value. Repeat for all rows below where predicted và observed values exist.


Now, these values could be positive or negative sầu.

4. Calculate the root mean square error value

In cell D2, use the following formula khổng lồ calculate RMSE:


Cell D2 is the root mean square error value. And save sầu your work because you’re finished.

If you have a smaller value, this means that predicted values are cthua lớn observed values. And vice versa.

What’s Next?

RMSE quantifies how different a set of values are. The smaller an RMSE value, the closer predicted & observed values are.

If you’ve tested this RMSE guide, you can try to lớn master some other widely used statistics in GIS:


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