Why by considering lasso regression, i.e.
$$\hat{\beta_1}, \hat{\beta_0} = arg\min_{\beta_0\, , \, \beta_1}\sum_{i=1}^n (y_i - \beta_1x_i -\beta_0)^2$$ with the constraint $\sum_{i=1}^p |\beta_i| \le\lambda$
we end up with sparsified coefficients?
Many thanks,
James