Lesson 16: Monte Carlo Simulation using Python vs Sheets

Review:

• Portfolios
• Grade Check
• Why you should love statistics (Ted Talk, 12 min)

Presentation:

• Coin Flip Simulation
  • Open your coin flip simulation in sheets
  • Think about what would be required to run the simulation 10,000 times (instead of 100)
• Python Simulation of Coin Toss in 3 steps
  • Step 1
  • Step 2
  • Step 3

Activity:

• Write a python program to simulate a coin toss 10,000 times
• Run the program successfully and save a screen capture showing the code, output and your name
• Use the output to generate a line graph and save the graphic
• Add to your portfolio

Assignment:

• How would you modify the coin toss simulation program to simulate rolling two dice?
• Hint: random.randint(1,6)

Lesson 15: Monte Carlo Simulation

Review:

• Random Variables
• Stock Market Simulation
• Portfolio 2 due today

Presentation:

• Monte Carlo Simulation
  • Lecture by John Guttag (MIT OpenCourseWare)

Activity:

• Use your Stock Market Simulation
• Generate a 95% Confidence Interval to estimate your retirement savings at age 65.
• For example, you might estimate your ending balance will be $200,000 +/- $50,000 with 95% confidence
• Write your confidence interval on your Portfolio (by hand is fine).
• If done correctly, I will award up to 6 points of extra credit to your Portfolio score (out of 100).
• [Note: you must attend class to take advantage of this opportunity]

Assignment:

• Enjoy your Spring Break!

Lesson 14: Random Variables and Stock Market Simulation

Review:

• Probability Models
• Dice Simulation
• Portfolio due Wed
  • Lessons 7-10,12-14 (7 lessons total, including today)
  • Min 2 pages, Max 4 pages

Presentation:

• Random Variables
  • Discrete Random Variables
    • Probability distribution table
    • Dice Simulation

    • 

  • Continuous Random Variables
    • Area under a density curve (e.g., Normal Curve)
    • Stock Market Simulation
      • How to simulate a normal distribution in Sheets
      • Using Annual Stock Market Return data

Assignment:

• Watch Video from Unit 20 – Random Variables
• Create a Stock Market Simulation in Sheets using the Monthly return data
  1. Calculate the number of months until your 65th birthday
  2. Generate a simulation with the number of months calculated in step 1.
  3. Use $10,000 as your starting balance
  4. Run a test simulation (or a few) to be sure the numbers are making sense
  5. When ready, run the simulation 30 times and save the ending balance from each simulation (you’ll have 30 separate ending balances).
  6. Calculate the mean and standard deviation of your n=30 ending balances
  7. Make a histogram of your ending balances
  8. Create a portfolio slide summarizing your results

Lesson 13: Probability Models and Dice Simulation

Review:

• Intro to Probability
• Portfolio due next week
  • Lessons 7-14
  • 2-page min, 4-page max
  • Due Wed

Presentation:

• Probability Models
  • Video
• Sample Space
  • Discrete vs Continuous
  • All possible Outcomes
• Probability Rules (see p. 246 in textbook)
  • Rule 1: Any probability is a number between 0 and 1. Or, mathematically, 0 ≤ P(A) ≤ 1
  • Rule 2: All possible outcomes together must have probability = 1.
  • Rule 3: If events A and B have no outcomes in common, they are disjoint and P(A or B) = P(A) + P(B). This is the addition rule.
  • Rule 4: The complement of an event, A = 1 – P(A)
  • Rule 5: If events A and B are independent then P(A and B) = P(A)*P(B). This is the multiplication rule.
• How to calculate discrete probability:
  • Step 1: Define the Sample Space (all possible outcomes)
  • Step 2: Identify the set of outcomes that satisfy Event A
  • Step 3: P(A) = Number of Event A outcomes ÷ Number of possible outcomes
  • Example:
    • Roll a pair of dice
      • Define Event A (e.g., roll = 7). What is P(A)?
      • Follow Steps 1-3 above
      • Step 1: 36 possible outcomes
      • Step 2: Roll a 7 with 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 (6 possible outcomes resulting in a roll of 7)
      • Step 3: P(A): 6/36 = 1/6 = 0.167
• Demonstrate Simulation of rolling a pair dice in Sheets
  • Lucky 7 game
    • Roll a 7, win bet
    • Roll anything else (other than a 7), lose bet

Assignment:

• Create your own Dice Simulation
  • Replicate the “Lucky 7” game
  • Modify rules so you win when you roll doubles
  • Decide on appropriate “payout odds” (2x, 3x, 4x, 5x?) for rolling doubles
    • Give the “house” a slight advantage

Lesson 12: Intro to Probability

Review:

• Exam 2 Results
• Review Exam 2
• Top Models (R Square, F Statistic)
  • Scott M. (0.756, 752.9)
  • Denin M. (0.749, 725.2)
  • Sam B. (0.746, 713.9)
  • Daniel G. (0.737, 680.8)
  • Ju Hyeok P. (0.736, 679.5)
  • Daniel S. (0.724, 867.1)

Presentation:

• Intro to Probability
  • Topic worthy of its own course
  • Simulation of outcomes
    • Random phenomenon
      • Individual outcomes are uncertain
      • Regular distribution of outcomes in large number of trials
  • Video
  • Demonstrate Coin Toss Simulation in Sheets

    • 

Activity:

• Create your own Coin Toss Simulation in Sheets
• Replicate the chart above
• Add to your portfolio

Exam 2 Results

Lesson 11: Review for Exam 2

Review:

• Dummy variables
• Exam 2 in class on Wed
• See instructions for Exam 2 Part 1

Presentation:

• Exam 2 Review Topics
  • Multiple Regression
  • Interpretation of Regression Output
    • R^2
    • Coefficients > y-hat equation
    • t-statistics and associated p-values (individual variable significance)
    • F-statistic and associated p-value (overall model significance)
  • Multicollinearity
  • Interaction Variables
  • Dummy Variables
  • Produce y-hat estimate given x values

Assignment:

• Complete Exam 2 Part 1
• Study for Exam 2

Exam 2 Part 1 Instructions

Exam 2 Part 1 Instructions

For Exam 2 you will build a multiple regression model as a “take-home” project. You will use the model during the exam. The model should be complete and you should have a 1-page print-out in hand when you arrive for the exam. See below for details.

• Multiple Regression Analysis
  • Select the worksheet corresponding to the last digit of your PID from this file: PuebloRealEstate_Exam2Data_ByPID
  • Build a regression model to estimate selling price
    • You must use 1 interaction variable
    • You must use 1 or more Dummy variables
  • Prepare a 1-page summary of your model, including
    • Regression Output with highlights
    • y-hat equation (in equation format, not just a copy of the regression output)
    • Define the variables used in the model (if interaction, how is it calculated?)
    • Demonstrate how to apply the model
      • What “selling price” estimate would your model produce for a home in Belmont neighborhood, 3 bedroom, 2 bath, 1800 sqft
    • Think of your 1-page summary as a “poster” that explains your model
      • It should be clear and easy to understand
      • It should provide helpful text to explain different aspects of the model
  • Be prepared to answer questions about your regression model
  • You will use your model during Exam 2 and then turn it in after completion of the exam
  • Exam is “open notes” (so bring anything useful) but you may only submit the 1-page summary (I won’t accept a stack of different model outputs)

Lesson 10: Applied Regression Analysis (2 of 2)

Review:

• Variable Selection
• Real Estate Selling Price estimates/forecasts
• Exam 2
  • Part 1 – regression modeling project instructions (Mon Feb 25)
  • Part 2 – in-class exam with questions about your regression model (Wed Feb 27)

Presentation:

• Applied Regression Analysis
  • Dummy Variables
    • incorporate categorical variables
    • binary – value is either 1 or 0
    • if 0, then the coefficient has no effect on y-hat
    • if 1, then the coefficient is added to (or subtracted from) the estimate
  • Demonstration with Sample Real Estate data
    • create a dummy variable for a neighborhood

Assignment:

• Build a regression model to estimate Real Estate selling prices
  • Use this data set Pueblo RE East Side
  • Create and use a dummy variable for “Belmont”
  • Use your regression model to estimate selling prices for these 4 properties
    • Belmont 3 BR, 2 BA, 1600 SqFt
    • Belmont 4 BR, 3 BA, 2400 SqFt
    • East Side 3 BR, 1 BA, 1200 SqFt
    • East Side 2 BR, 1 BA, 800 SqFt
  • Add results to your Portfolio
    • Regression output
    • y-hat equation
    • 4 property Selling Price estimates

Lesson 9: Applied Regression Analysis (1 of 2)

Review:

• Exam 1 Retake
  • Results
  • Grading
• Multiple Regression Variable Selection
• Missing links on forward/backward selection replaced. Read this: Variable Selection
• DataCamp Invite Link

Presentation:

• Go through modeling process with 2013 MLB Team statistics data
• Applied Regression Analysis
  • Interaction Variables
    • combine separate variables mathematically
    • add, multiply, etc
    • another way to avoid problems with multicollinearity
  • Demonstration with Sample Real Estate data
  • Estimate selling price for a 1500 sqft, 3 bd, 2 ba home

Assignment:

• Build a regression model to estimate Real Estate selling prices
  • Use this data set Pueblo RE East Side
  • Use an interaction variable to avoid multicollinearity
  • Use your regression model to estimate selling prices for these 4 properties
    • Belmont 3 BR, 2 BA, 1600 SqFt
    • Belmont 4 BR, 3 BA, 2400 SqFt
    • East Side 3 BR, 1 BA, 1200 SqFt
    • East Side 2 BR, 1 BA, 800 SqFt
  • Add results to your Portfolio
    • Regression output
    • y-hat equation
    • 4 property Selling Price estimates