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Answer by einar for Incorrectly Using the Word "Causal" to Describe a...

There is a very careful formulation in Gelman, Hill, and Vehtari Regression and Other Stories:From the data alone, a regression only tells us about comparisons between units, not about changes within...

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Answer by mkt for Incorrectly Using the Word "Causal" to Describe a...

On average, a one unit increase in $x_i$causes is associated with an increase in $y_i$ of $\beta_1$ units.

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Incorrectly Using the Word "Causal" to Describe a Regression Model?

Suppose we take the classical linear regression model:$$y_i = \beta_0 + \beta_1 x_i + \epsilon_i$$Over the years, I have heard so many people say that such an interpretation can be drawn from this...

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