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In an A-Level maths textbook that I am reading about least-squares regression, it states that a regression line should only be used to predict the dependent variable and not the independent variable. I am looking for some intuition about this.

Naively, I would expect the regression line of $y$ on $x$ to be an inverse of the regression line of $x$ on $y$ . Specifically, I would expect the model $y_i = a + b x_i$ to produce an inverse model $x_i = -\frac{a}{b} + \frac{1}{b} y_i$.

Why is this not the case?

Bysshed
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  • The dependent variable is what you are predicting. It can make sense to change roles. For example, you could be interested in predicting statistics score for students from their algebra score, or vice versa. But you don't get the second regression by rearranging the regression equation obtained by the first. – Nick Cox Jul 16 '21 at 13:18
  • Note for many readers: A-level is an examination taken in the latter years of secondary school in Britain and in some other countries, typically by students at around age 18. – Nick Cox Jul 16 '21 at 13:20

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