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The R code is correct. You could also use the I() operator. You can look here on page 53. The code then would be lm(stock~market+I(market^2)+I(market^3), data=example) EDIT: going more into detail: Doing the above you define regressors $market^2$ and $market^3$. The coefficients will be calculated the usual way (covariance of response with the regressors ...

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