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# Python | Root mean square error

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Steps to find the MSE

1. Find the equation for the regression line.

(1)

2. Insert the X values ​​into the equation found in step 1 to get the corresponding Y values, i.e.

(2)

3. Now subtract the new Y values ​​(ie ) from the original values ​​of Y. Thus, the found values ​​are erroneous terms. This is also known as the vertical distance of a given point from the regression line.

(3)

4. Square the errors found in step 3.

(4)

5. Summarize all squares.

(5)

6. Divide the value found in step 5 by the total number of observations.

(6)

Example:
Consider these points: (1,1), (2,1), (3 , 2), (4,2), (5,4)
You can use this online calculator to find the equation / regression line.

Regression line equation: Y = 0.7X — 0,1

X Y
110.6
2 1 1.29
3 2 1.99
422.69
5 4 3.4

Now using the formula found for MSE on step 6 above, we can get MSE = 0.21606

MSE using scikit — learn:

`  Output:  0.21606 `

MSE using Numpy module:

` `

 ` from ` ` sklearn.metrics ` ` import ` ` mean _squared_error ` ` `  ` # Specified values ​​` ` Y_true ` ` = ` ` [` ` 1 ` `, ` ` 1 ` `, ` ` 2 ` `, ` ` 2 ` `, ` ` 4 ` `] ` ` # Y_true = Y (original values ) `   ` # calculated values ​​` ` Y_pred ` ` = < / code> [ 0.6 , 1.29 , 1.99 , 2.69 , 3.4 ]  # Y_pred = Y & # 39; ``   # Calculation mean square error (MSE) mean _squared_error (Y_true, Y_pred) `
 ` import ` ` numpy as np ` ` `  ` # Specified values ​​` ` Y_true ` ` = ` ` [` ` 1 ` `, ` ` 1 ` `, ` ` 2 ` `, ` ` 2 ` `, ` ` 4 ` `] ` ` # Y_true = Y (original values) `   ` # Estimated values ​​` ` Y_pred ` ` = ` ` [` ` 0.6 ` ` , ` ` 1.29 ` `, ` ` 1.99 ` `, ` ` 2.69 ` `, ` ` 3.4 ` `] ` ` # Y_pred = Y & # 39; ` ` `  ` # Mean square error ` ` MSE ` ` = ` ` np.square (np.subtract (Y_true, Y_pred)). mean () `
` `

` `

`  Output:  0.21606 `