Ok, in that case there is the cost function, defined on the model's parameters, that measures the average distance from the sample points to your hypothesis. This is the average error the model has for the fixed parameters. In the case of linear regression, the importance of a certain variable is given by the weight parameter attached to that variable.

If you are familiar with multidimensional calculus, the dependence of a fixed such parameter is given by the partial derivative of the cost function in this direction.

This is quite well explained in Andrew Ng's video lecture on linear regression: https://www.youtube.com/watch?v=pkJjoro-b5c&list=PLLssT5z_DsK-h9vYZkQkYNWcItqhlRJLN&index=19.