# Calculation of RMSE (standard deviation) in R

I have numeric watch functions `V1`

through `V12`

taken for a target variable `Wavelength`

. I would like to calculate the RMSE between columns `Vx`

. The data format is below.

Each "Vx" variable is measured at 5 minute intervals. I would like to calculate the RMSE between observations of all Vx variables, how to do this?

This is the link I found, but I'm not sure how I can get y_pred: https://www.kaggle.com/wiki/RootMeanSquaredError

For the link below, I don't think I have any predicted values: http://heuristically.wordpress.com/2013/07/12/calculate-rmse-and-mae-in-r-and-sas/

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For your help, just wrote these functions:

```
#Fit a model
fit <- lm(Fertility ~ . , data = swiss)
# Function for Root Mean Squared Error
RMSE <- function(error) { sqrt(mean(error^2)) }
RMSE(fit$residuals)
# If you want, say, MAE, you can do the following:
# Function for Mean Absolute Error
mae <- function(error) { mean(abs(error)) }
mae(fit$residuals)
```

Hope this helps.

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## How to perform RMSE in R.

See my other canonical 97+ answer, voted to do RMSE in Python: fooobar.com/questions/101114 / ... Below I will explain it using R code terms.

RMSE: (root mean square error), MSE: (root mean square error), and RMS: (root mean square error) are all mathematical tricks to sense the change over time between two lists of numbers.

RMSE provides one number to answer the question, "How similar are the numbers from list1 to list2 on average?" The two lists must be the same size. I want to "wash the noise between any two given items, wash the size of the collected data and feel one number change over time."

## Intuition and ELI5 for RMSE:

Imagine you are learning how to throw darts at darts. Every day you train for one hour. You want to find out if you are getting better or worse. Therefore, every day you make 10 throws and measure the distance between the bull's eye and the point where the dart hits.

You are making a list of these numbers. Use the root mean square error between distances on day 1 and a list containing all zeros. Do the same on the 2nd and 9th day. What you get is one number that will hopefully decrease over time. When your RMSE number is zero, you hit the bullets every time. If the number goes up, you get worse.

## **An example of calculating the root mean square error in R:**

```
cat("Inputs are:\n")
d = c(0.000, 0.166, 0.333)
p = c(0.000, 0.254, 0.998)
cat("d is: ", toString(d), "\n")
cat("p is: ", toString(p), "\n")
rmse = function(predictions, targets){
cat("===RMSE readout of intermediate steps:===\n")
cat("the errors: (predictions - targets) is: ",
toString(predictions - targets), '\n')
cat("the squares: (predictions - targets) ** 2 is: ",
toString((predictions - targets) ** 2), '\n')
cat("the means: (mean((predictions - targets) ** 2)) is: ",
toString(mean((predictions - targets) ** 2)), '\n')
cat("the square root: (sqrt(mean((predictions - targets) ** 2))) is: ",
toString(sqrt(mean((predictions - targets) ** 2))), '\n')
return(sqrt(mean((predictions - targets) ** 2)))
}
cat("final answer rmse: ", rmse(d, p), "\n")
```

What prints:

```
Inputs are:
d is: 0, 0.166, 0.333
p is: 0, 0.254, 0.998
===RMSE Explanation of steps:===
the errors: (predictions - targets) is: 0, -0.088, -0.665
the squares: (predictions - targets) ** 2 is: 0, 0.007744, 0.442225
the means: (mean((predictions - targets) ** 2)) is: 0.149989666666667
the square root: (sqrt(mean((predictions - targets) ** 2))) is: 0.387284994115014
final answer rmse: 0.387285
```

## **Mathematical notation:**

## RMSE is not the most accurate line fitting strategy, total least squares:

Root mean square error measures the vertical distance between a point and a line, so if your data is banana-shaped, flat at the bottom, and steep at the top, then the standard deviation will report long distances to high points, but short distances to points low when at the very top. In fact, the distances are equivalent. This causes skewing where the line prefers to be closer to the points above than below.

If this is a problem, the general least squares method fixes it: https://mubaris.com/posts/linear-regression/

## Corrections that may break this RMSE functionality:

If any of the input lists contain zeros or infinity, then the rmse output will be meaningless. There are three strategies to deal with zeros / missing values / infinities in any list: ignore this component, zero it out, or add best guess or uniform random noise for all time steps. Each drug has its own pros and cons depending on what your data means. In general, it is preferable to ignore any component with a missing value, but this shifts the standard deviation towards zero, making you think that performance has improved, when in fact it is not. Best guess random noise may be preferable if there are many missing values.

To ensure that the RMSE output is relatively correct, you must eliminate all zeros / infinities from the input.

## RMSE has zero tolerance for rogue data points that do not belong

The root mean square error is based on the correctness of all data, and they are all considered equal. This means that one random dot in the left margin will completely ruin the whole calculation. To handle outlier data points and reject their huge impact beyond a certain threshold, see robust estimates that construct a threshold for outlier rejection.

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You can either write your own function or use the hydroGOF package which also has an RMSE function. http://www.rforge.net/doc/packages/hydroGOF/rmse.html

As for your y_pred, you first need the model that created them, otherwise why would you want to compute the RMSE?

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