本次美国代写是关于数学相关的一个Assignment

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

Y  X1+X2+X3+X4+X5+X6+X7+X8+X9+X10+X11+X12+X13+X14

Y: BIO
X1: H2S
X2: SAL
X3: Eh7
X4: pH
X5: BUF
X6: P
X7: K
X8: Ca
X9: Mg
X10: Na
X11: Mn
X12: Zn
X13: Cu
X14: NH4

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

Y: BIO
X2: SAL
X4: pH
X7: K
X10: Na
X12: Zn

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

selection procedure.

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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