# Does the choice of error function impact the model parametrs?

Suppose I have trained a multi variate linear regression model on a particular training set, and the model parameters $$\theta=[\theta_1,\theta_2,\ldots, \theta_n]$$ were determined by minimizing a cost function, say MSE (Mean Squared Error).

Now, if for some reason I decide to change my choice of error function from MSE to MAE (Mean Absolute Error), will this change my model parameter $$\theta$$ or will it remain the same?