Welcome to BUAD 310

1. Welcome to BUAD 310 Instructor: Kam Hamidieh Lecture 10, Wednesday February 19, 2013

2. Agenda & Announcement • Today: • Finish up from last time • Parts of Chapters 13 and 14. • Talk about Exam 1 • Note: Homework 3 is due tomorrow 8 AM. BUAD 310 - Kam Hamidieh

3. Exam 1 • It will be in class on Wednesday February 26, 2014. • It will cover everything up to the end of today’s lecture. • You’ll have 33 multiple choice questions & use Scantron. I’ll pass out the Scantron sheets next time. • Exam cover sheet will be up on Monday. • Last year’s first exam, and a set of practice problems with solutions will be posted. • We’ll spend 2/24 doing a few review problems. • From our syllabus “You may bring a single handwritten sheet (both sides) containing formulas to each test …. No make-ups of tests will be given. You will receive a grade of zero for each missed test unless you have a written excuse from your doctor or the University.” • No communication devices are allowed. However, you can use your phone as a calculator or bring a simple calculator. BUAD 310 - Kam Hamidieh

4. Exam 1 • These are the *only* things you need to bring to the exam: • Scantron sheet filled out • Pencil for the Scantron sheet • Eraser • Z-Tables • Calculator • Cheat sheet, hand written, both sides ok • I will provide you with everything else including scratch paper. BUAD 310 - Kam Hamidieh

5. Last Time • Inverse problems: • A probability p, 0 ≤ p ≤ 1, is given. • Find x so that P( X ≤ x ) = p. • The little p is called the pth quantile of X. • The joint probability distribution of two or more random variables: P(X = x and Y = y) = p(x,y) • All the rules we learned with probabilities apply to random variables. • Correlation ρ (rho): A measure of linear dependence between random variables. BUAD 310 - Kam Hamidieh

6. In Class Exercise 1 (Prob 33 & 35 in your book) Let X and Y be two random variables with Cov(X,Y) = 12500, and the means and standard deviations as given below. Find the expected value and SD of the following random variables derived from X and Y. • 2X-100 (hint: see lecture 8, slide 5) • 0.5 Y (hint: see lecture 8, slide 5) • X + Y (hint: see lecture 9, slide 18) BUAD 310 - Kam Hamidieh

7. (Sample) Correlation for Data • Suppose we have a data set with the daily return for IBM and Microsoft. See the snippet below:X = IBM ReturnsY = MSFT Returns • How would we find the correlation for X and Y? We do not know the joint probability distribution of X and Y! AdjClose.IBM.returnsAdjClose.MSFT.returns 2003-01-03 0.013 0.001 2003-01-06 0.023 0.018 2003-01-07 0.029 0.019 2003-01-08 -0.021 -0.028 2003-01-09 0.033 0.028 2003-01-10 0.008 0.002 BUAD 310 - Kam Hamidieh

8. SAMPLE Correlation for Data It can be shown that we can get an “estimate” of the correlation by using the following formula: BUAD 310 - Kam Hamidieh

9. A Closer Look Just good ole means of the data! “weighing” is 1/(n-1) Just good ole SD of the data! BUAD 310 - Kam Hamidieh

10. Quick Example (Go over on your own!) BUAD 310 - Kam Hamidieh

11. Same Interpretation as Before… • It is a good measure of linear dependence of two random variables(now in data columns). • Always true: -1 ≤ Corr(X,Y) ≤ +1 • Values near: • 1 mean strong positive correlation • 0 mean week linear correlation • -1 mean strong negative correlation • Correlation is unit-less. BUAD 310 - Kam Hamidieh

12. Some Correlations BUAD 310 - Kam Hamidieh

13. IBM vs MSFT BUAD 310 - Kam Hamidieh

14. The Circle BUAD 310 - Kam Hamidieh

15. Our Survey Data BUAD 310 - Kam Hamidieh

16. An Interesting Application • Companies like Amazon.com, Netflex, Google, and many more like to make recommendations to their customers. Why? • What should they recommend to a specific customer? • Item based: watch what customers buy, and “associate” items bought with other “similar” items • Individual based: find “similar” customers • A combo of the above • How do you measure similarity between two customers? BUAD 310 - Kam Hamidieh

17. Correlation as a Measure Similarity Pick two at a time & find the correlation between each person’s data and use that correlation as a measure of similarity. Take 94826’s numbers and 68245’s and find correlation. > main.data Lego AwkwardMomentVampireAcad L-Survivor Frozen AmericanHustleTheWolf Her Sinbad 5numbers 20 2 3 2 2 5 3 4 4 0 23985 48 0 2 0 4 5 3 4 1 0 94826 79 4 0 1 0 5 3 4 0 0 25431 94 0 3 0 5 5 2 4 0 0 68245 BUAD 310 - Kam Hamidieh

18. Analysis Continued The Lone Survivor Frozen The Wolf of Wallstreet That Awkward Movement 94826 and 68245 are quite similar!  American Hustle Her BUAD 310 - Kam Hamidieh

19. Analysis Continued 94826 and 68245 are most similar: Cor = 0.95 BUAD 310 - Kam Hamidieh

20. Some More Rules • Extended addition rule for expected value of sums:E(aX + bY+c) = aE(X) + bE(Y)+c • Extended addition rule for variance of independentrv’s:Var(aX + bY+c) = a2Var(X) + b2Var(Y) • Extended addition rule for variances:Var(aX+ bY+c) = a2Var(X) + b2Var(Y) + 2abCov(X,Y) BUAD 310 - Kam Hamidieh

21. Example • Suppose X ~ N(0,2) and Y ~ N(2, 4), and Corr(X,Y) = -0.50. • Find the mean and standard deviation of 3X – 2Y + 7:Cov(X,Y) = Corr(X,Y) × SD(X) × SD(Y) = (-0.5)(2)(4) = -4E(3X – 2Y + 7) = 3E(X) – 2E(Y)+7 = 3(0)-2(2)+7= 3Var(3X – 2Y + 7) = 9Var(X) + 4Var(Y) + 2(3)(-2)Cov(X,Y)Var(3X – 2Y + 7) = 9(4)+ 4(16) +2(3)(-2)(-4) = 148 SD(3X – 2y + 2) = square root of 148 ≈ 12.17 • Would the answer change if I had not told you that the random variables were normal? BUAD 310 - Kam Hamidieh

22. In Class Exercise 2 (Prob 33 & 35 in your book) Let X and Y be two random variables with Cov(X,Y) = 12500, and the means and standard deviations as given below. Find the expected value and SD of the following random variables derived from X and Y. • 2X + Y • X + Y + 2Y – 2X • Can you think of a real life scenario where (2) could apply? BUAD 310 - Kam Hamidieh

23. Next Time • We do Exam 1 Review. BUAD 310 - Kam Hamidieh