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Josh field landscaping

https://jobs.cashierjobs.com/jobs/atlanta/19/jobs/JOO_5199/2018-09-27/1012370490172/

JOO needs land scape company to install 6 living walls in their familys area. They are willing to negotiate after the property is purchased to have us keep the \$ with a completed home and high bizness apron,\$1,500 if the job is to start no later than end of december. Interested in how many years they need us to maintain the job and their responsibilites. Looking at new jobs? JOO has great location and money paying the company to build the jobs next year. they have 700 bizness aprox \$10000-\$13000

Here we discuss two research methods called factor analysis and cluster analysis. While I am going to be using R for these examples it is a generalizable method.

Principal Component Analysis

Often when working with multivariate data we want to reduce our data to an uncorrelated set of variables which can be summarised. The example above shows the 22 jobs taken from the data where the relationship between the variables is not clear (see image below). So lets look at the data in a new way. We want to look at what variables are important in describing the response variables. We use Principal Component Analysis (PCA) to find a new set of linearly uncorrelated variables.

The process is not perfect and because the process is slightly ill-defined there are many different methods for PCA. I will use the factor analysis method for simplicity in R as there is no easy way to import the files from the analysis. Factor analysis for an exploratory data analysis is more used than cluster analysis but I will use a similar method to get the factors in R and see how they come up.

Factor Analysis Exploratory Data Analysis

The first step is to find a rotation so that the variables are ordered and the squared error for a single variable is small. A typical rotation is to make a new matrix which is multiplied by the column matrix (one row) of the data.

# factor analysis # coef function of the PCA # making the variable corr matrix columns are not square of data of factors >, 0, # varimax with Kaiser normalization , varimax function does not preserve the signs of the original variables

When looking at the items and factors produced using PCA the easiest way to order them is to look at the variance explained. If we need to rotate factors higher variance explained needs to be a criteria. A rotation where there is no correlation is fairly close to all variances of a factor explained and this usually changes when there is some correlation between factors. The use of the items to create the correlations is a requirement.

# create the correlation matrix from the data set # cor function >, 0 # corr.any matrix with negative correlations will be rotated # var.rotate function will rotate the data but not correlation structure

The components are the first few eigenvectors that are orthogonal and an important (usually the first) set. The rotated matrix which creates a correlation between the factor can be converted back to the original variable space by a covariance matrix.

# covariance matrix of the rotated vector # correlation matrix # scatter graph for the rotated variance % of the items # principal components % of the rotated variance # rotated % of the total % of variance

To actually construct the principal components using R you use the function prcomp. It is important to be aware of how the principal components are constructed. The first principal component is the vector which has the most variance in the system. The rest are orthogonal to each other and can be thought of as being orthogonal principal components as well.This can be understood by looking at the example below.

# PCA # m = matrix of the data set # m = matrix of the rotated vectors # 1 means the row is the first factor # 2 means the column is the first factor # factorgram(m) PCA = princomp(m) # 2nd eigenvector # plot(PCA\$loadings) # see the 2nd eigenvector # eigenvalues is the eigenvalue

So what does the eigen

1. Aubrey

The first is something

2. Shacage

Small zhzhot)))) yyyyyyyyyy

3. Raidyn

What words ... the imaginary

4. Akinogrel