SAS CODES

• SAS CODE for Data Split

Regression Projects

• Group 1:
  • Data: Real Estate Sales
  • Descrption of data: Appendix C.7 in textbook ALSM
  • Analysis Objective: The city tax assessor was interested in predicting residential home sales prices in a mid-western city based on the demographic variable information given in Appendix C.7 in textbook ALSM.
  • Learning Objective: The full scope of multiple linear regression which involves model fitting, model selection, model diagnosis, model remedy and model validation.Nonparametric regression technique based on regression trees.
  • Analysis Guildline :
    • Select a random sample of 300 observations to use in the model-building data set. Develop a best subset model for predicting sales price. Justify your choice of model. Assess your model's ability to predict and discuss its use as a tool for predicting sales prices.
      • Prepare separate dot plots for each of the predictor variables. Are there any note worthy features in these plots?
      • Tentatively decide upon the functional form of the regression relations ( whether given variables are to appear in linear form, quadratic form, ect.) and whether any interaction terms are to be included.
      • Obtain three of the "best" subsets ( you can use any model selection procedures) of potentially useful predictor variables to be included in the final regression model.
      • Check the three "good" regression models in detail for curvature and interaction effects. Residual plots are helpful in deciding whether one model is to be preferred over another.
      • Obtain scatter plot matrix, correaltion matrix of the selected variables and the variance inflation factors. Are there any indication that serious multicollinearity problems?
      • Obtain the studentized deleted residuals and prepare a dot plot of these residuals. Are there any outliers present?
      • Obtain the hat matrix and use the rule of thumb in the text of ALSM to identify any outlying X observations
      • Obtain DFFITS, DFBETAS, and Cook's distance values for the cases that are outlying with respect to their X values or Y values to assess their influence.
      • Does the diagnostics analysis indicate remedial measures may need to be taken?
    • The regression model identified should be validated by means of the validation data set consisting of those cases not selected for the model-building data set.
      • Fit the regression model identified above to the validation data set. Compare the estimated regression coefficients and their estimated standard errors with those obtained by fitting to the model-building data set. Also compare the error mean square and coefficient of multiple determination. Does the model fitted to the validation data set yield similar estimates as the model fitted to the model-building data set?
      • Calculate the mean square prediction error and compare it to MSE obtained from the model-building data set. Is there evidence of a substantial bias problem in MSE here?
    • Develop a regression tree for predicting sales price. Justify your choice of number of regions (tree sizes), and interpret your model. Assess your model's ability to predict and discuss its usefullness as a tool for predicting sales prices. Compare the performance of your regression tree model with that of the best regression model obtained earlier. Which model is more easily interpreted and why?
• Group 2:
  • Data: Real Estate Sales
  • Descrption of data: Appendix C.7 in textbook ALSM
  • Analysis Objective: The city tax assessor was interested in predicting residential home sales prices in a mid-western city based on the demographic variable information given in Appendix C.7 in textbook ALSM.
  • Learning Objective: The full scope of multiple linear regression which involves model fitting, model selection, model diagnosis, model remedy and model validation. The nonlinear regression technique based on neural network model.
  • Analysis Guildline :
    • Select a random sample of 300 observations to use in the model-building data set. Develop a best subset model for predicting sales price. Justify your choice of model. Assess your model's ability to predict and discuss its use as a tool for predicting sales prices.
      • Prepare separate dot plots for each of the predictor variables. Are there any note worthy features in these plots?
      • Tentatively decide upon the functional form of the regression relations ( whether given variables are to appear in linear form, quadratic form, ect.) and whether any interaction terms are to be included
      • Obtain three of the "best" subsets ( you can use any model selection procedures) of potentially useful predictor variables to be included in the final regression model.
      • Check the three "good" regression models in detail for curvature and interaction effects. Residual plots are helpful in deciding whether one model is to be preferred over another.
      • Obtain scatter plot matrix, correaltion matrix of the selected variables and the variance inflation factors. Are there any indication that serious multicollinearity problems?
      • Obtain the studentized deleted residuals and prepare a dot plot of these residuals. Are there any outliers present?
      • Obtain the hat matrix and use the rule of thumb in the text of ALSM to identify any outlying X observations.
      • Obtain DFFITS, DFBETAS, and Cook's distance values for the cases that are outlying with respect to their X values or Y values to assess their influence.
      • Does the diagnostics analysis indicate remedial measures may need to be taken?
    • The regression model identified should be validated by means of the validation data set consisting of those cases not selected for the model-building data set.
      • Fit the regression model identified above to the validation data set. Compare the estimated regression coefficients and their estimated standard errors with those obtained by fitting to the model-building data set. Also compare the error mean square and coefficient of multiple determination. Does the model fitted to the validation data set yield similar estimates as the model fitted to the model-building data set?
      • Calculate the mean square prediction error and compare it to MSE obtained from the model-building data set. Is there evidence of a substantial bias problem in MSE here?
    • Develop a neural network model for predicting sales price. Justify your choice of number of hidden nodes and penalty function weight, and interpret your model. Assess your model's ability to predict and discuss its usefullness as a tool for predicting sales prices. Compare the performance of your neural network model with that of the best regression model obtained above. Which model is more easily interpreted and why?
• Group 3:
  • Data: Real Estate Sales
  • Descrption of data: Appendix C.7 in textbook ALSM
  • Analysis Objective: The city tax assessor was interested in knowing which the demographic variables affect the quality construction of houses in a mid-western city.
  • Learning Objective: The full scope of multiple logistic regression which involves model fitting, model selection, model diagnosis, model remedy and model validation.
  • Analysis Guildline :
    • Create a new binary response variable Y, called high quality construction, by letting Y=1 if quality (variable 10) equals 1, and Y=0 otherwise (i.e., if quality equals 2 or 3). Carry out a complete logistic regression analysis, where the response of interest is high quality construciton (Y), and the pool of predictors includes sales price, finished square feet, number of bedrooms, number of bathrooms, air conditioning, garage size, pool, year built, style,lot size,and adjacent to highway (variables 2 through 9 and 11 through 13). The analysis should consider transformations of predictors, inclusion of second-order predictors, analysis of residuals and influential observations, model selection, goodness of fit evaluation, and the development of an ROC curve. Develop a predicion rule for determining whether the quality of construction is predicted to be of high quality or not. Model validation should also be employed. Assess the strengths and weakness of your final model.

The analysis guildlines suggest certain research questions and analyses to help you to achieve the study objective. If you wish, you may propose your own questions and carry out somewhat different analyses. For the project you choose, you may work individually or choose to work with one other person and submit a joint project. If you choose to work jointly, both people will receive the same grade for the project and it is up to both partners to make sure that the work is shared equitably. Groups larger than two are not permitted. Your project should be submitted in the form of a paper (typed) which describes the problem, the analyses you carried out, and your findings. Your SAS results should appear as tables or figures, either in an Appendix, or in the text (for the most important ones). All output should be clearly labelled, and edited to remove non-essential portions. Do not simply tack on a pile of output through which the reader will have to wade to find the relevant analyses. As a general rule, do not include any output which you do not mention, describe or discuss in the text of your paper.

Regression Project Report

The quality of the written report on your analysis will figure prominently in the grading. You will be marked to some extent on what would be expected in a professional consultation or research report. You may choose to deviate somewhat from the following outline, but this is roughly what I expect. (See Ehrenberg, 1982, "Writing Technical Papers or Reports", The American Statistician, 36, 326-329, for further suggestions.)

1. Abstract. This should consist of a brief statement (a paragraph) summarizing the purpose or goal of your study, and the results and what they mean, in substantive rather than statistical terms. As Shakespeare said, brevity is the soul of wit!-- be brief and to the point, stimulating your reader's interest.
2. Introduction. This should include a clear statement of your view of the scientific question(s) of interest in connection with your data. The goals of the statistical analysis should be clear to all who read this section. Because there will be notable variability in the amount of background information available with the data sets, there will necessarily be variability in the levels of detail appropriate for the analyses. (Background reading in the applied subject area will be useful in some cases.)

   Begin with a statement of a problem or question to be investigated, then introduce the data.

   Following the introduction of the problem or question try to provide motivation for the analysis to follow:

   • What kind of data is relevant to studying the question?
   • Which variables might be expected to be relevant predictors? Why?
   A formal research study might be expected to state explicit hypotheses. You may not have any, but at least try to suggest which variables might be expected to be useful, relevant or important predictors.
3. Methodology. The methodology, results, and discussion should focus on the question you studied, rather than on a catalog of steps of analysis or of tables of results.

   Describe here the models and methods used to analyse your data. If necessary, explain why the methods are appropriate and how you looked at the data to examine assumptions, justify transformations, etc. Be specific. (``MPG was transformed to -1/MPG, and log(PRICE) was used to achieve a linear relation'' rather than ``some variables were transformed''.) What methods were used to select your final model? Omit description of general aspects of statistics-- assume your reader knows what a multiple regression model is.

4. Results. Results of analyses should be presented simply and clearly. Use graphical displays, tables, and discussion. Undigested computer output is not appropriate here. Reference to figures, tables or labelled points in computer output in an appendix may be useful. It is not necessary to write out formal tests of hypotheses as you would on an assignment -- this is supposed to be a research report.
5. Interpretation and/or Discussion. The questions to be addressed are: Does the prediction equation make sense? Do the predictors seem reasonable? What do the signs and magnitudes of the regression equations mean?

   This section should also describe the scientific and statistical issues raised by the results described in the preceding sections. Suggestions for further analysis or other data are appropriate. Summarize (again) your conclusions about the scientific questions and back up your assertions with references to your Results: graphs, tables, etc.

6. Appendices. There can be one or more appendices. You will probably want to include at least one appendix logging the details of the computations. The output should be trimmed and annotated. You do not need to include the raw data.

   All output should be labeled (e.g., Fig. 1, Table 10, or Exhibit 2) and referred to in the text (eg., "see Exhibit 2"). Output should be summarized where possible or compressed (deleting uninformative stuff), rather than just inserted whole, especially where it deals with subsidiary issues.

7. Style. I do not insist on any specific formatting style, but here are some tips:
   • Use headings for each section/subsection consistently, and effectively to communicate the structure of your ideas, as well as their content. You need not follow the headings suggested above slavishly.
   • Make it easy for the reader by refering to specific page, table, figure, etc. in the text to indicate where the relevant information may be found.
   • Cite sources (where appropriate) in the text as Author (year), putting bibliograpic sources in a References section at the end (before the Appendix)

Experiment Design and Analysis Projects

• Data: Real Estate Sales
• Descrption of data: Appendix C.7 in textbook ALSM
• Analysis Objective: Analyze a series of experiments to investigate how house construction quality, style and number of bedrooms affect the house sales price.
• Learning Objective: How to design a powerful experiment and using ANOVA techniques comprehensively for balanced and unbalaned design.
• Analysis Guildline :
  • Predictor Variables
    • Quality

                      		Actual level    Quality variable
                      		----------    -------------
          				  1-2                1
                                        3                  0
                                                          
         				                    		   	
                                  

    • Number of Bedroom

                      		Actual level    Bedroom# variable
                      		----------    -------------
          				 0-2                   0
                                       3                     1
                                       4 or more             2  	   				   		   	                                                  
                                  

    • Style

                      		Actual level    Bedroom# variable
                      		----------    -------------
          				 1                   1
         				 not 1               0
                                    
                                  

  • Response Variable: house sales price
  • Your total design should include three experimental runs, together with suitable analysis of each:

    RUN=0 : One (or more) pilot studies with NOBS <= 4 observations for each group in your design. That is, random sampling 4 observations for each group combinaton (total 2 by 3 by 2 = 12 group combinations) from the given real estate sales data and carry out a complete balanced analysis of variance. Also consider if tansformations of the response variable is necessary. You should use pilot study to examine your choice of sample sizes required for each group combination.

    Note: The MSE from an analysis of variance of your pilot data and The maximum and minimum factor level means for a given factor can be used for power/sample size analysis of that design.

    RUN=1 : The main study, with a design determined from your pilot data. The number of observations per group should be chosen based on your power and sample size analyses from pilot data. We would like to achieve a power of at least .80 for the three main effects and for all the possible interaction. Random sample the determined number of observations from the given real estate sales data and carry out a complete banlanced three way analysis of variance. Also consider if tansformations of the response variable is necessary.

    RUN=2 : A replication study - must include the same overall design as the main study, but you may use different sample sizes. The data should be sampled from the given real estate sales data excluding the data used in RUN=1. The purpose of the replication study is simply to determine if your findings from RUN=1 hold up when the study is conducted again. Ideally, the significant findings from your main study should appear again in the replication.

    RUN=3: As a comparison,assume that the sample sizes do not reflect the importance of the treatment means. Carry out an complete unbalanced three-way analysis of variance of the entire real estate sales data using the same response variable and three predictor variables discussed above. The analysis should consider transformations of the response variable.

    RUN=4: As an another comparison, assume that the sample sizes reflect the importance of the treatment means. Carry out an complete unbalanced three-way analysis of variance of the entire real estate sales data using the same response variable and three predictor variables discussed above. The analysis should consider transformations of the response variable.

  How to write up the project

  It is very important to provide a clear and complete TYPEWRITTEN write up for this project. An earlier section (Analysis guildline) provide a short summary of what is expected. The following is one suggestion on how you can organize the text of the project.

  The main objective is to document how you designed the study and teased out the results. The most important aspect of the project write up is your description of what you did (and why) and your summary of the results. Remember: PLEASE DO NOT HAND IN MORE THAN 15 PAGES OF COMPUTER OUTPUT.

  The following outline suggests the topics to focus on in your writeup.

  1. Introduction: What is this project all about?
     1. The Study: Describe, very briefly, in your own words, the background behind the experiment.
     2. Your Task: Summarize the method you used to run these experiments, and the steps involved (i.e., pilot, experiment, and replication runs, etc.).
  2. Pilot Work:
     1. Discuss the logic you used to select each of pilot runs. In particular, what did you learn from one experiment which caused you to change your design for the next?
     2. Discuss the results from your various pilot runs.
  3. Main Experimental Runs
     1. What patterns did you find in the pilot data which led to your choice of an experimental design? Consider the following issues:
        • sensitivity to all relevant main effects and interactions
        • efficiency of the design
        • sample size
     2. Run 1: The Experimental Run. Discuss the results of your main experiment, considering the following:
        • main effects and interactions
        • contrasts
        • fit of the model and departures
        • outliers
     3. Run 2: Replication Study. Discuss consistencies and inconsistencies with run 1.
     4. Run 3: The Comparison Run. Discuss the results and considering the following:
        • main effects and interactions
        • contrasts
        • fit of the model and departures
        • outliers

          Discuss consistencies and inconsistencies with run 1.

     5. Run 4: The Comparison Run. Discuss the results and considering the following:
        • main effects and interactions
        • contrasts
        • fit of the model and departures
        • outliers

          Discuss consistencies and inconsistencies with run 1.

  4. Summary of Results: Integrate all your findings from the pilot, run1, run2, run3 and run4.
  5. Conclusion: What conclusions can you give? This should be directly related to the study. Example: How do sales price change when you vary quality, number of bedrooms and style?