Hospital Sale Report Programming by Rstudio Economics Essay

Please follow these guidelines when you write your reports.
1. Project Outline
Title Page: Must contain
Project title.
Your names and group number
Date.
Executive Summary. ( very short and to the point).
The executive summary contains a brief account of your conclusion. Write the results not the description of the problem. Say: I found that the IBM price stock was at a higher level in October than in November, in October the mean price was ......
Introduction: If any, must be very short. Describe your project and give the background information. Try to be brief but at the same time do not leave out the relevant information. Here you include the basic descriptive statistics, graphs and summaries of the data. Please if you have several graphs or large tables put them in an appendix and refer to them on the text.
Methods: (not needed)
Usually where you describe the statistical methods that will be applied. You don’t need it here because methods are in the class notes.
Analysis and Results:
Give a graph or table describing the process that you follow to conduct your analysis and the steps that you overtook. Give also a description of these steps on the text.
State your points or hypotheses and prove them or disprove them. Go point by point showing performing the corresponding hypothesis tests and interpreting the results. If you use a computer software that generates a sizable output file, put the output file as an appendix and refer to the output here for performing your hypothesis tests.
Conclusion: Like the executive summary but longer. Establish the connection between the statistical results and the practical conclusion as they relates to our case study.
References: List of books or articles that are cited on the text. If you do not cite any then omit it (you are not required to have it).
Appendix: Should contain your code, graphs, tables and figures. Every table graph and figure should have a title with a number such as Table 1. The title should explain with precision the content of the table or figure. Table titles goes on top of the table. Title for figures and graphs goes at the bottom. Try to underline and number the places in the output that are quoted in the above text and use those numbers to refer to that piece of output in the text.
The reports that you will write in this class will be no more than 4 or 5 pages of written text plus a few more of output. The output should be organized in tables + charts, but never append a thick printout. However, a reasonable report should be as brief as possible.
If your report length is 15 pages or less in total, including appendices and everything, then you should be fine. But if you have more pages than 15 you should try to cut or reduce the appendices or other parts. For example, your code can be presented in a two-column table with font 9pt or 8pt so that it occupies very little space.

Final Report:

(Due May 8 but possibly extended to May 10-12)

SALES OF ORTHOPEDIC EQUIPMENT

The objective of this study is to find ways to increase sales of orthopedic products from our company to all hospitals in the United States.   Find those who have high consumption of such equipment but where our sales are zero. Come up with a selected group where you think our efforts will be rewarded. (a few hospitals 5 or 10 or 15). Estimate the potential or expected sales on those hospitals.

The following description of the dataset includes variable names and some summaries of variable.

At the bottom of the file is also some additional R code.

Dataset: hospitalUSA.csv
VARIABLES:

     ZIP :  US POSTAL CODE
     HID :  HOSPITAL ID
    CITY :  CITY NAME
   STATE :  STATE NAME
    BEDS :  NUMBER OF HOSPITAL BEDS
   RBEDS :  NUMBER OF REHAB BEDS
   OUT-V :  NUMBER OF OUTPATIENT VISITS
     ADM :  ADMINISTRATIVE COST(In $1000's per year)
     SIR :  REVENUE FROM INPATIENT  

   SALES : SALES OF EQUIP in $1000's per year
     HIP :  NUMBER OF HIP OPERATIONS
    KNEE :  NUMBER OF KNEE OPERATIONS
      TH :  TEACHING HOSPITAL?  0, 1
  TRAUMA :  DO THEY HAVE A TRAUMA UNIT?  0, 1
   REHAB :  DO THEY HAVE A REHAB UNIT?  0, 1
    HIP2 :  NUMBER HIP OPERATIONS Year 2
   KNEE2 :  NUMBER KNEE OPERATIONS Year 2
  FEMUR2 :  NUMBER FEMUR OPERATIONS Year 2

Overview of the Analysis

Part 1. Select your market segment-s.

1.    Dataset: hospitalUSA.csv set.seed(????) set.sed(23456) use you Rutgers id (5 last digits)

 Every student of has his/her own data (it is enough to select about 3000-3500 hospitals at random). Set the zero values on SALES to missing values.

Separate the variables into the following groups:

Response:             SALES, SALES=0 => SALES=NA

Demographics:      BEDS, RBEDS, OUTV, ADM, SIR, TH, TRAUMA, REHAB  

Operation numbers:  HIP, KNEE, HIP2, KNEE2, FEMUR2

2.  Transformations:

Look at each individual variable and decide "if and which" transformation is appropriate. Some transformations are log(1+c*x) where the constant c changes from variable to variable ( 0.1,0.01,0.001,…) or sqrt transformation or any other.

Typical transformations should be of the type below but not exactly, so you need to try several possibilities for each variable until the histogram looks acceptable.

HIP = sqrt(HIP)  or    SALES = log(1+0.1*SALES)

3.  Dimension reduction.

Use the factor method to summarize the demographic variables and the operation variables and come out with a final reduced list of factor variables (perhaps 3 or 4). Use the rotated factors in order to find a good interpretation of the factors and try to make a good story.

library(psych)

## Scree plot

barplot(fa(rr1,nfactors=15)$Vaccounted[5,],col=7)

abline(h=0.75,lwd=3,col=2)

### Run factor analysis using correlation matrix

### Use Varimax rotation

fit <- fa(rr1,nfactors=6,rotate="varimax")

## After checking output assign variables to

##  factors

apply(fit$loadings,1,function(x) which.max(abs(x)))-> fn

4.   Market segmentations.  

i) Independent variables are used to divide the list of hospitals (all possible clients = the market) into subsets which we call market segments or clusters.
Use cluster analysis to find the market segments or clusters. Since we are summarizing the variables with factors then use the factors. One way of choosing the number of clusters is to move the data into R and apply the silhouette function with pam to calculate the silhouette statistic and of cluster it to decide the number clusters. Then move the cluster variable back to SAS if you prefer.

ii) Once the clusters are chosen, we must study the summary statistics for each cluster and try to describe their content. Interpretation is very important at this stage. You do a boxplot of SALES or transformed SALES VS CLUSTER_NUMBER and choose clusters with the highest SALES and focus on the top cluster or clusters.

iii)      Finally, we select the cluster or clusters that agree with our objectives. These are clusters with high sales and with good characteristics, such as high number of operations, etc.

In this study you are looking for segments with over all high sales but where there are hospitals were the company's sales is NA so they are not yet our customers. Some segments will have mostly low sales. This means that those hospitals have few patients who would need our products, so we are not interested in them.

Part 2. Estimating potential gain in sales. Potential gain in sales is the difference between current sales and the average of sales to similar hospitals. If you are analyzing a very small cluster (N <100) then we might assume that the sales are homogeneous and the “average sales to similar hospitals” is just the average sale to that cluster. But if the cluster is larger than 100, we will need to redo the clustering with more clusters.   Methods: 1. Pam, 2. Kmeans, 3.HC using Ward.

Selecting the numbers of clusters 15-30 using silhouette criteria , second der, GAP statistic.

We are interested in hospital with no current sales that is NA sales. For these hospitals

your estimate of the potential gains is the average sales for that cluster.

All these parts could be performed using R. The R analysis would apply the methods for robust clustering (pam) and for classification and regression trees (rpart)  4^th method.

PAM: compare the clusters given by PAM with those from SAS, are they similar?

RPART: The idea here is to take the SALES variable that was defined earlier as a response. Run the tree method and select one good node that have very high sales and find hospitals on that group that have SALES=NA and estimate a potential sale gain.

Use the rpart package in R. The rpart function is similar to lm in the sense that it accepts “predict” for new data. Please use more than 14 clusters not 14 or less.

2. Something about your writing style
Paragraph Structure: When you write a paragraph try to be organized. A way to do this is to start by saying the thesis, then follow with a list of arguments that prove it, quoting the output, performing hypothesis tests, etc. Finally reinforce the result.
Say the thesis.
Prove it.
Say it again.
Another way to construct paragraphs is by using concatenation: from A prove B , from B prove C, and so on.