Mean squared error loss with python code

**mean squared error (mse) loss**

mean squared error (mse) is a commonly used loss function in regression problems. it calculates the average of the squared differences between the predicted values and the actual values. the lower the mse value, the better the model's performance.

the formula for mean squared error is:

\[ mse = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y_i})^2 \]

where:
- \( n \) is the number of samples
- \( y_i \) is the actual value
- \( \hat{y_i} \) is the predicted value

in python, you can calculate mean squared error using libraries such as numpy. here is an example code that demonstrates how to calculate mse:

in this code:
1. we import the numpy library.
2. we define the actual values and predicted values as numpy arrays.
3. we calculate the mean squared error by subtracting the actual values from the predicted values, squaring the differences, and then taking the mean.
4. finally, we print the calculated mean squared error.

you can use this code as a reference to calculate the mean squared error for your regression models in python.

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