Suppose that linear regression is used to estimate factorial effects for a $2^{k}$ design by doubling the

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Suppose that linear regression is used to estimate factorial effects for a $2^{k}$ design by doubling the estimated regression coefficients.

a. When is it possible to estimate the standard error of these regression coefficients?

b. If the p-values for the regression coefficients are able to be calculated, then is it necessary to transform these p-values to correspond to p-values for factorial effects? Explain.

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