本次作业是来自美国的主要是关于一个统计分析project的数学代写
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