OM Project

I want to buy a boat. I know, only idiots and fools buy boats, but I want to join that unique group of water skimmers. Since I want to minimize my idiocy I only want to look at used boats (let someone else take that depreciation). Since there are a whole lot of different types and brands of boats we are going to have to set some limitations or we’ll never get this narrowed down. Let’s suppose that we are only interested in boats ranging from 18 to 26 feet. In addition we are only going to look at three brands of boats: Bayliners, Searays, and Greenville’s own Grady Whites.

Given the wealth of available information on the prices of boats on the Internet, your project is to develop a multivariate regression equation using the price of a used boat as your dependent variable. You may use either the asking or final selling price as your dependent variable. The independent variables on which to gather data include:

1. Age of boat
2. Length of boat
3. Motor size
4. Number of engines
5. Bowrider vs. center console
6. Brand of boat (Bayliner, Searay, Grady White
7. Motor type (inboard vs. outboard)

And any other variables you feel relevant to the analysis.

The objective of this project is to build the best regression equation possible, given the data sampled. You must randomly sample at least 25 boats for each brand. Be sure that your statistical analysis includes at a minimum the following:

1. an original correlation matrix
2. hypothesis tests of each independent variable included in your final equation.
3. any relevant statistical plots.
4. an evaluation of your overall model.
5. interpretations of the coefficients of the significant independent variables in the model.
6. a discussion of any problems encountered in building the model and how they were resolved. (if applicable).
7. a discussion of how the model could be used and any suggestions for improving the model if possible if the project was repeated in the future. Be sure that in your discussion you describe the source of your data, the date sampled, etc.
   

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   Project Issues
   Just a few guidelines so you can avoid some common problems on the project.
   1. you should be including higher order terms like rate of increase and interaction. The real world rarely moves in a straight line. Theoretically, you would not expect age to be linear for example. As a boat gets older it depreciates, but it will eventually level off. The same with length. As far as interaction, the impact of motor size or age on price could depend on length. Theoretically most large boats have large motors (brick), so we may not find much of an effect in large homes. But we see a lot more variance in motor size with smaller boats. We would expect to see a bigger impact in these boats. Now you may not find that any of these are significant in your sample, that’s ok as long as you tried them. To code higher order terms you use Transform, Compute on the menu bar. Then just name your variable and multiply the variable by itself (for square term) or by another variable (for interaction). SPSS will place the new variable in the first blank column.
   2. Don’t use first person in your writeup. This should be like a business report.
   3. To determine whether a bigger or smaller model is significant you should use the test of reduced vs. complete models that we had on the first test. That’s why we covered it.
   4. Note that there is a guide to writing up the project. It is handout 10. Make sure that you do not discuss every single thing that you did to come up with your final model.
   5. There is an explanation on Blackboard as to how to code dummy variables. Common dummy variables for this project are type of brand, bowrider, motor type, etc.
   6. If you have references (and you should at least for data collection), then reference them. On the first case not many of you actually referenced your references.
   7. If you have higher order terms don’t worry about correlations or VIFs between them and their lower order term. Of course a square term is going to be correlated with its lower order term. Multicollinearity rules don’t count then.

To save us some pain and me some writing on your drafts I am going to give some generic comments:

1) Your introduction should be a real one and cover boating and why someone might desire a used boat. Also need a purpose statement.

2) You should mention how you sampled (random sampling) in your data section and have a table that shows how you coded the data.  Make sure you code brand correctly.

3) Model development should go like this: run with first order terms, get rid of multicollinearity, fix any problems like hetero or outliers, do F-test of reduced vs complete model until you have best lower order model. This means that if you have insignificant variables at this point remove them one at a time and run the model.  Do the F-test of reduced vs. complete.  Repeat if necessary.

4) Add higher order terms one at a time, if they are significant then leave them in the model. When you add one variable and it is significant that is the same as if you did a reduced/complete F test. You’ll end up with a model with 3-4 lower order and maybe 1 or 2 higher (that is in general, every data set is different). YOU CAN’T HAVE A HIGHER ORDER TERM LIKE AGESQ IF YOU DON’T HAVE AGE IN THE MODEL. It’s not a line anymore. At the end of your model development do the F test of reduced vs complete against your original model.

5) Discuss your results. Tell me what 1 year of age does to price. Do that in a table or something. Be careful if you have higher order terms. If you have a negative age term and a positive age square term then you are limited in how you can discuss it. You have to say age has a negative effect on price but that effect lessens as age increases.

5) If you have to do a log transformation of y then you will have to take the antilog to discuss it. There are 2 downloads in the BB site about this.

6) At the end discuss what you found and the limitations. Discussion consists of a) what you found, b) what the limitations are, c) what else would need to be done to help.

This is a business paper. The purpose is to help someone buy a boat. Your conclusion should say what the most important factors are if one wants to buy a boat.  This has to make sense. If you tell me that a year of age adds $ to a boat you are wrong. Same

When you read your paper if you see endless discussion of blow by blow statistics then it isn’t correct. If you want to do that put it in a appendix and reference it. You can just say something like: The common variance assumption was violated and a log transformation was performed. The transformation corrected the problem and all other assumptions were satisfied. A discussion of the assumption tests can be seen in Appendix B.

I need to see your original and final model output from SPSS. You can cut and paste them into an appendix. That should include your diagnostic statistics.

By the way, the correct way to code manufacturer is:
To code categories, 3 categories, 2 dummies, coded as follows:


actual
observation     GW   SR

GW                         1      0

SR                            0      1

BL                            0      0

The year of the boat should be coded as age. In other words don’t code it 2001, code it 9 years old.

Price: $31.52

Solution: The downloadable solution consists of 21 pages, 1052 words and 3 charts.
Deliverable: Word Document