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A statistician wishes to consider 4 explanatory variables for a particular modelling exercise using multiple linear regression. They decide to consider the full model and all subsets. (a) How many models are considered in total? (b) Explain why Adjusted R² might be preferred to R² when comparing these models. (c) Write down a formula for Mallow's Statistic for a model with k ≤ 5 parameters defining all of the terms that you use and explain how any unknown values in the formula are estimated. (d) Explain two ways in which Mallow's Statistic can be used to select a model with the reasoning for each method. New data is available to the statistician so that 8 explanatory variables can now be considered. Model selection is now undertaken by an automated approach. (e) Explain carefully the steps needed to select a model by Stepwise Regression (sometimes called Modified Forward Regression) including how you would estimate the variance of residuals.

A statistician wishes to consider 4 explanatory variables for a particular modelling exercise using multiple linear regression. They decide to consider the full model and all subsets. (a) How many models are considered in total? (b) Explain why Adjusted R² might be preferred to R² when comparing these models. (c) Write down a formula for Mallow's Statistic for a model with k ≤ 5 parameters defining all of the terms that you use and explain how any unknown values in the formula are estimated. (d) Explain two ways in which Mallow's Statistic can be used to select a model with the reasoning for each method. New data is available to the statistician so that 8 explanatory variables can now be considered. Model selection is now undertaken by an automated approach. (e) Explain carefully the steps needed to select a model by Stepwise Regression (sometimes called Modified Forward Regression) including how you would estimate the variance of residuals.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A statistician wishes to consider 4 explanatory variables for a particular modelling exercise using multiple linear regression. They decide to consider the full model and all subsets. (a) How many models are considered in total? (b) Explain why Adjusted R² might be preferred to R² when comparing these models. (c) Write down a formula for Mallow's Statistic for a model with k ≤ 5 parameters defining all of the terms that you use and explain how any unknown values in the formula are estimated. (d) Explain two ways in which Mallow's Statistic can be used to select a model with the reasoning for each method. New data is available to the statistician so that 8 explanatory variables can now be considered. Model selection is now undertaken by an automated approach. (e) Explain carefully the steps needed to select a model by Stepwise Regression (sometimes called Modified Forward Regression) including how you would estimate the variance of residuals.
Transcribed Image Text:A statistician wishes to consider 4 explanatory variables for a particular modelling exercise using multiple linear regression. They decide to consider the full model and all subsets. (a) How many models are considered in total? (b) Explain why Adjusted R² might be preferred to R² when comparing these models. (c) Write down a formula for Mallow's Statistic for a model with k ≤ 5 parameters defining all of the terms that you use and explain how any unknown values in the formula are estimated. (d) Explain two ways in which Mallow's Statistic can be used to select a model with the reasoning for each method. New data is available to the statistician so that 8 explanatory variables can now be considered. Model selection is now undertaken by an automated approach. (e) Explain carefully the steps needed to select a model by Stepwise Regression (sometimes called Modified Forward Regression) including how you would estimate the variance of residuals.
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