Solution (source code)

= Solution
{c}

If the two regressors are strongly associated, the data may provide little support for varying one while holding the other fixed. <Multicollinearity> makes the separate slope estimates unstable, and exact <linear dependence> makes them unidentifiable. A conditional slope may also be an extrapolation beyond combinations actually observed.

Furthermore, a slope in a <linear regression model> is not automatically a <causal effect>. A causal interpretation needs appropriate design or assumptions excluding <confounding>; independence of the errors across observations and zero mean alone do not establish those assumptions. The coefficients describe the specified linear mean relation, but changing a regressor by intervention can have a different interpretation.