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Let's assume we have the following simple linear regression equation:

y = 10 - 4.2x

Let's further assume that our response variable y is expressed in units of 100 kilograms. Let's also assume that our independent variable x is expressed in currency.

Is it correct to say that for every 1-unit change in currency x, that our y response variable will decrease by 420 kilograms?

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  • $\begingroup$ Yes, the inference from regression is scale invariant meaning the predicted response line will be the same whether the units are transformed before the response is input the regression model, or if the predictions are transformed after fitting the regression model. $\endgroup$
    – AdamO
    Mar 1, 2022 at 19:29
  • $\begingroup$ @AdamO please see my answer on what I think OP should change $\endgroup$
    – jros
    Mar 1, 2022 at 19:33

1 Answer 1

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You are almost correct to interpret the regression coefficients this way. Instead of saying "for every 1-unit change" there is a decrease, it should be: "For every 1-unit increase in currency" there is a decrease. Specifying the direction of the relationship is important for readers.

A more pedantically correct way to interpret these coefficient relationships would be:

"For every one unit increase in currency, the expected y decreases by 420 kgs. For every one unit decrease in currency, the expected y increases by 420 kgs."

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