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Assume that we have p covariates X and we want to fit a linear model without an intercept. Prove that the effective degrees of freedom

Assume that we have p covariates X and we want to fit a linear model without an intercept. Prove that the effective degrees of freedom for linear regression estimated using least squares is equal to p. Remember that effective degrees of freedom is calculated by taking the trace of the matrix S, such that our predictions can be written as Yhat = SY

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