Session 5 - Lecture notes 1 PDF

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Prof: Richard Crabb...

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Session 5: Data Relationships, Probability 9-19-18 In excel: Enter Correlation and r squared as a % .7453 >> 74.53 .5561 >> 55.61 Covariance How do we calculate correlation? We need to know the covariance Covariance measures how much the movement in one variable predicts the movement in a corresponding variable Covary inversely: downward sloping trendline Not very useful HAS A UNIT (first unit) * (second nit) Covariance= average of the product of deviation Won’t be tested ((E with n on top and i=1 on bottom)(Xi-Xbar)(Yi-Ybar))/n In excel= COVAR Calculating Correlation (Covariance (X,Y)) / (StDev(X) * StDev(Y)) Summary: Covariance Measures the strength and direction of a linear relationship b/w 2 variable Sensitive to the units of x and y so it's hard to interpret We use correlation instead Summary: Correlation Unitless measure of relationship that's unaffected by measurement scale Always b/w -1 and +1 Very rough rule of thumb: strong/weak cutoffs at < .3 and > .7 Can be sensitive to outliers Excel: CORREL

Things to Remember -A correlation is a single number summary of a scatterplot. It never conveys as much info as the full scatterplot -You are usually on the lookout for large correlations, those near -1 or +1 -Don't try to interpret covariance, except possibly to check if its pos or neg. For interpretation, focus on correlation

Why Study Probability? Decision makers must manage risk How should car insurers calculate premiums How should the IRS decide who to audit How should UW Madison budget it's resources based on how much they think they’ll get from gov Probability is essential to understanding risk Enables risk analysis, sensitivity analysis Easy to make mistakes w/o basic knowledge Monty Hall and Probability 3 doors. One has a car you can win First pick: 1 in 3 chance When you have two doors left, you have 50% of being on the right door If you switch, you win ⅔ of the time If you stay, you win 1/3 of the time *problem like this on exam* Probability 101  A probability is a number between 0 and 1 that measures the likelihood that some event will occur  Probabilities are often expressed as percentages  Higher the probability of something, the more likely it is for it to happen We name our events with letters Ex. A The probability with which this happens is P(A) Chances that Crabb will pick a name from row 1 is A The complement of A is the opposite of A and is denoted P(Abar) Abar= A with a horiz line above it Can also be denoted P(A’) Can often be easier to calculate the complement so it's nice for that P(A’)= 1- (# names in row 1)/# names in class Examples P(A’)= 1 - P(A) P(get an ace of spades in 3 draws)= P(Ace of spades on draw 1) + P(Ace of spades on draw 2) + P(Ace of spades on draw 3) = 1- P(ace of spades not drawn in 3 draws)

= 1- 51/52 * 50/51 * 49/50= 1 - 49/52 P(At least 1 shared a birthday among 3 people)= 1- P(0 shared) = 1- ((364/365) * (363/364))...