# Appraise the statement: “For the model 𝑦 = 𝛽0 + 𝛽1𝑥 + 𝑒, 𝛽1 reflects the causal effect of 𝑥 on 𝑦.” Ask

not sure if this was the right place to ask my question, but I saw some questions regarding linear regression so I'd thought I would try to get some answers here. I just started learning about linear regression so this is the homework posed to me.

I assume that the statement is true since 𝛽1 is the coefficient for 𝑥. And its the coefficient that would determine if the slope (i.e. the relationship) is positive or negative.

Am I missing out anything or what should I expound on?

Thanks for reading and for the guides and opinions.

You have two aspects here. In principle you are right that $$\beta_1$$ is the slope of $$x_1$$ (you can say the marginal effect of $$x_1$$ on $$y$$) and $$\beta_0$$ is the intercept. This is simply a linear function of form $$f(x)=\beta_0 + \beta_1 x$$.
However, to claim "causality", a few more things are required. First, you need to make the assumption that there is a causal relation between $$x$$ and $$y$$ and $$x$$ must be exogenous.
Another important aspect is, that if there are additional variables with a causal influence on $$y$$, say $$x_2$$, you cannot really claim that $$\beta_1$$ is the causal effect on $$...$$, because you omitted $$x_2$$, so that your model suffers from the omitted variable bias. To claim for causality you need to make sure that your model reflects the data generating process in a proper way.