I. PROJECT DESCRIPTION
In this project, you will analyze the Linthurst data and identify the important physic-ochemical properties of the substrate inﬂuencing the aerial biomass production in the Cape Fear Estuary of North Carolina.
The response variable Y is BIO (the biomass production), and there are 14 predictor variables characterizing the soil. For instance, SAL is the percentage of salinity and pH is the acidity in the water, etc.
There are 45 observations. The ﬁrst column is the index of the observation, the second column Loc” and the third column ”Type” are not used in this project.
The full multiple linear regression model is
The project includes three parts.
A. Part I
Consider the 14-predictor data set (LINTHALL.txt). Use the ordinary least square estimation to estimate the regression coefﬁcients. Run the collinearity diagnostics and identify if there is any collinearity.
B. Part II
Consider the 14-predictor data set (LINTHALL.txt). Use the Principle Components Regression method with collinearity reduction to decide which principle components will be included in the model. From the results of Principle Component Regression, compute the regression coefﬁcients in the original multiple linear regression model.
C. Part III
In Part III, we consider a smaller data set (LINTH-5.txt) for convenience. The full multiple linear regression model is:
Y X2 + X4 + X7 + X10 + X12
The data set only has 5 predictor variables, and yet it preserved some of the collinearity problem. We will use the 5-predictor data set (LINTH-5.txt) to perform a variable
1) Use the stepwise regression method to decide the best model. Use signiﬁcance level E = R = 0:15. At each step, report the result of regression, indicate which predictor variable enters or leaves the model, and how the decision is made.
2) Use the subset selection method to decide the best two-variable model on the basis of Cp. If there is a tie, use VIF to break the tie.
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