If ridge regression biases ALL beta coefficients of a regression model towards zero, wouldn't the model massively mispredict the y-variable?
I know my logic must be wrong here, but I'd appreciate if someone could point out the flaw. I am just starting to get into this topic, so would appreciate as simple an answer as possible.
For example: Say you have the coefficients of a linear regression output (and for simplicity, all coefficients are positive, and say the x-variables can only take on positive values). Then, if you biased each beta coefficient towards zero, wouldn't the model consistently underpredict the y-variable?
Would appreciate any intuition on how ridge regression shrinks all the coefficients but still maintains predictive ability. Thank you!