What is Mallows Cp equation?

What is Mallows Cp equation?

• A. Cp = (1/n) * (SSE + 2p*MSEfull)
• B. Cp = SSE/n + p*MSEfull
• C. Cp = (SSE + p*MSEfull)/n
• D. Cp = SSE/(n-p)

Answer: (A)

Mallows Cp is a model-selection tool for linear regression that balances how well a model fits the data with how complex (many predictors) the model is. It uses the residual sum of squares from the candidate model (SSE) and the mean square error from the full model (MSE_full) as a baseline for the noise. The term 2 p MSE_full acts as a penalty for including p parameters in the model, and dividing the sum by n scales the statistic to be comparable across sample sizes. When a candidate model is truly a good subset of the full model, Cp tends to be close to the number of parameters p. Thus the form (SSE + 2 p MSE_full) / n captures both lack of fit and the cost of added complexity, making it the best choice among the options. The other forms don’t appropriately combine SSE and the penalty term or fail to scale correctly with n, so they don’t reflect Mallows Cp as intended.

Mallows Cp is a model-selection tool for linear regression that balances how well a model fits the data with how complex (many predictors) the model is. It uses the residual sum of squares from the candidate model (SSE) and the mean square error from the full model (MSE_full) as a baseline for the noise. The term 2 p MSE_full acts as a penalty for including p parameters in the model, and dividing the sum by n scales the statistic to be comparable across sample sizes. When a candidate model is truly a good subset of the full model, Cp tends to be close to the number of parameters p. Thus the form (SSE + 2 p MSE_full) / n captures both lack of fit and the cost of added complexity, making it the best choice among the options. The other forms don’t appropriately combine SSE and the penalty term or fail to scale correctly with n, so they don’t reflect Mallows Cp as intended.