Projects

Submission Guidelines

• Submit your project by sending it as a PDF file attachment to the email address:

   adiky at gradcenter.cuny.edu

• The subject should specify:

   CSC 21700: PROJ # Student name

• The file name of the attached work should be following:

  LastName-FirstName-PROJ#-CSC21700.pdf

  • LastName is your last name

  • FirstName is your first name

  • # is a project number

• Work should be submitted no later then 11:59pm of a due date.

• If you copy, you will receive a zero points.

• Work must be submitted as a PDF formated file. No links or files in any other document format is allowed. Make sure that your file is no more the 20 Mb, so you'll be able to send it as an email attachment.

• Do not expect a reply on your email after the submission, you would be contacted if it's necessary.

There is 5% penalty if your work does not comply with above guidelines.

Project 1: Porfolio Simulation

• Due date: November 17.

You can choose to invest your money in one particular stock or put it in a savings account. Your initial capital is 1000 dollars. The initial stock price is 100 dollars. The interest rate $r$ is 0.5% per month and does not change. Your stochastic model for the stock price is as follows:

• next month the price is the same as this month with probability 1/2,

• with probability 1/4 it is 5% lower,

• and with probability 1/4 it is 5% higher.

The principle applies for every new month. There are no transaction costs when you buy or sell stock.

Your investment strategy for the next 5 years is:

• convert all your money to stock when the price drops below 95 dollars,

• and sell all stock and put the money in the bank when the stock price exceeds 110 dollars.

Describe how to simulate the results of this strategy for the model given.

• Determine number of simulation so the Monte Carlo study would attain the margin of error ±0.01 with probability 0.99.

• How does this strategy compared to gains from the savings account for the same period of time? Determine success rate the above strategy related to gains from the savings account.

• Calculate 95% confidence interval for estimated strategy success rate.

Assume another investment strategy when you put money in stock when price drops below 100 dollars and sell these stocks when price is above 115 dollars.

• Is there a significant difference between two strategies?

• Is it true that the difference between strategies is less then 50 dollars?

Formulate and test the hypotheses at a level $\alpha = 0.05$.

You should submit a small report for your project. A well-documented source code of your project should be added to the report appendix section.

Project 2: Regression

• Due date: December 17.

1. Generate individual dataset by following instructions in the Regression Project notebook.

2. Perform visual analysis of the data and investigate the relationship by constructing a scatter plot. Summarize findings.

3. Construct a linear regression model of your sample data.

4. Select 10% sample by picking every 10th value from the population and perform inference analysis calculations:

   • ANOVA table

   • ANOVA F-test

   • Confidence interval of the slope

   • Confidence interval for the mean of responses

5. Submit your report, as PDF document, with results of visual data and regression analysis, as well as inference results for the selected dataset.

   • INCLUDE HASH AND GENERATED POPULATION DATASET (predictors and response points) INTO YOUR REPORT

Below is a detailed outline of the content that could be included in your project report. The components are listed in outline form so that they can be used as a checklist. However, your project report is expected to be a formal paper (not an outline). Your results should be stated in complete sentences, and your paper should be written in paragraph form. Although you may choose to use headings, you should not number your paragraphs.

1. Introduction. State the topic of your study as a research question and/or as a specific hypothesis to be tested. For example, your hypothesis should indicate what type of correlation you expected to see (positive or negative) and how strong you expected the correlation to be (weak, moderate, strong). Your hypothesis should describe a specific result that you expected to find and the practical reason that you expected this result (your rationale).

2. Define Population. Define clearly the population(s) that you intend for your study to represent.

3. Define Variable(s). Define clearly the variable(s) that are analyzing.

4. Study Design. Identify statistical procedures you used to analyze your data. Give relevant design details (e.g., which variable was selected as the explanatory variable, and which the response variable? Why? What type of correlation did you expect? And so on.)

5. Results. Descriptive Statistics. You should give descriptive statistics for each of your two quantitative variables. Note that you will be reporting summary statistics for both your explanatory variable and your response variable. You could report each set of descriptive statistics using both a table and a chart as described below. All tables and charts should be placed directly in your report.

   • Table: Give sample size, mean, standard deviation, and a 5-number summary for each variable (minimum, first quartile, median, third quartile, and maximum).

   • Chart: Show boxplots that illustrates the distribution of each variable.

6. Results. Statistical Analysis. Report the results of your analysis; you could include following items:

   • Scatter plot with a graph of the regression line

   • Value of the correlation coefficient r and interpretation of its meaning

   • Equation of the regression line

   • An example of a prediction using the regression equation

   • Correlation value for the regression model and interpretation of its meaning

   • ANOVA table

   • Confidence intervals

7. Findings. Interpret the results of your statistical analysis in the context of your original research question. Do your analyses support your expected findings? Explain.

8. Discussion. What conclusions, if any, do you believe you can draw as a result of your study? If the results were not what you expected, what factors might explain your results? What did you learn from your project about the population(s) your studied? What did you learn about the research variables? What did you learn about the specific statistical analysis you conducted?