I have seen several practice questions using a simple linear regression eg y = ax + b where the question indicates that using a supplied value of y to find the x variable is invalid because the regression equation is the "wrong way round" ie can only be used to estimate a y value given the x value. I dont understand this. Surely it is just a line and it doesnt matter which axis you start from ie from x axis to get y or vice versa. What exactly is the issue here?
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See the linked thread. You missed that the model is $y = ax + b + \varepsilon$, where $\varepsilon$ is the noise term. – Tim Apr 12 '22 at 13:40