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This is a theoretical question, but I am working on an assignment that gives me a regression formula for wage when compared with years of experience. The regression formula is in the form: $\hat{w} = 4.7 + .23x - .004x^2$, where $\hat{w}$ is the predicted hourly wage. The question is asking what happens to the coefficients when you change the scale from hourly to weekly wage (40 hours in a week). My thinking is to treat this like any other polynomial function and multiply the $x^2$ coefficient by 40 to scale it "wider". Is this the proper way of thinking? Also, my guessing is that the t-test value or the critical value will also change. But by what factor?

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