I am dealing with the following exercise:
Exercise. In a linear regression model of the form $y = w_1x + w_0$, if we increase the value of $x$ by one unit, what can we expect from the value of of $y$?
$(a)$ An increase of value equal to $1$;
$(b)$ An increase of value equal to $w_0$;
$(c)$ An increase of value equal to $w_1;$
$(d)$ It is impossible to tell anything about the increase on $y$.
My attempt. As an aspirant to be a mathematician, this question leads to one simple line of thinking: if $x$ is increased by one unit, one might think of this as a simple variable change of the form $x \to x+1.$ If this is case, we obviously expect $y$ to suffer an increase of value equal to the parameter $w_1,$ hence I would select option $(c).$
My concerns. After some further thought, what exactly is "one unit" of the variable $x$? As far as I am concerned, this might not be a concept as objeticve as I thought. This makes me think that probably option $(d)$ makes some sense aswell.
All the information I have about the question is posted in the Exercise. section. Thanks for any help in advance.