# Impact of individual features under multi-collinearity

Assume the following scenario:

1. I have four features: $$x_1$$, $$x_2$$, $$x_3$$, and $$x_4$$
2. There are non-negligible multi-collinearity among the features.
3. I want to predict $$y$$ (response variable) with those 4 features.
4. I use simple multiple linear regression model: $$y = a_1x_1 + a_2x_2 + a_3x_3 + a_4x_4$$

Let's say that I want to understand the impact that different components of a chair have on the chair's retail price. For example:

$$y\,\,\,$$ = chair's retail price

$$x_1$$ = type or color of cushion used

$$x_2$$ = overall design of a chair

$$x_3$$ = strength of a chair

$$x_4$$ = softness of a chair

$$x_1$$ is completely independent, but other features are all somewhat impacted by the other features due to multi-collinearity, and their relationships are complicated. I've heard that the analysis of regression coefficients are unreliable under severe multi-collinearity.

Assuming that the multiple regression model fits the chair price well, can I naively use each feature's regression coefficient to understand the impact of each feature on the response variable? If not, what technique should I use?

Ex 1: If I use a red cushion ($$x_1$$), I can increased the retail price by 3 dollars

Ex 2: If I use conference room style chair ($$x_2$$), I can increase the retail price by 12 dollars