Class 6 Louie F1F6 - FORECASTING 1 Week 6 Statistical Analysis AGENDA 2 test of goodness of fit 13.1 Linear regression 14.1 14.2 14.3 14.5 Final

Class 6 Louie F1F6 - FORECASTING 1 Week 6 Statistical...

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FORECASTING Week 6 Statistical Analysis 1 9 / 2 6 / 1 5
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AGENDA 2 test of goodness of fit – 13.1 Linear regression – 14.1, 14.2, 14.3, 14.5 Final schedule 2 9 / 2 6 / 1 5
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2 TEST FOR GOODNESS OF FIT 3 9 / 2 6 / 1 5
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Suppose we have the following data from interviewing people in New York City: Prefer Diet Coke: 30% ( p 1 =0.3) Prefer Diet Pepsi: 25% ( p 2 =0.25) Prefer Regular Coke: 30% ( p 3 =0.3) Prefer Regular Pepsi: 15% ( p 4 =0.15) You ask 200 people in Baltimore the same question and get this answer: Prefer Diet Coke: 50 Prefer Diet Pepsi: 40 Prefer Regular Coke: 60 Prefer Regular Pepsi: 50 4 9 / 2 6 / 1 5
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ARE THE RESPONSES IN BALTIMORE SIGNIFICANTLY DIFFERENT FROM RESPONSES IN NEW YORK CITY OR DO THEY FOLLOW THE SAME DISTRIBUTION? 5 9 / 2 6 / 1 5
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2 TEST FOR GOODNESS OF FIT H 0 : probabilities in Baltimore are also p 1 , p 2 , p 3, p 4 H a : at least one of the probabilities in Baltimore differs from p 1 , p 2 , p 3, p 4 6 9 / 2 6 / 1 5
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2 TEST FOR GOODNESS OF FIT Can Reject H 0 7 9 / 2 6 / 1 5 81 . 7 17 ) ( ) ( 2 05 . 0 2 4 1 2 2 1 2 2 i i i i k i i i i E E f = E E f =
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2 TEST FOR GOODNESS OF FIT When to use: To test if the data comes from a specified distribution. 1. Test the following null and alternative hypotheses: H 0 : the population has a specified distribution H a : population does not have the specified distribution 2. Define k intervals for the test 3. Record observed frequency (f i ) for each interval and calculate expected frequency (E i ) 4. Calculate the chi-square statistic 8 9 / 2 6 / 1 5
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EXAMPLE 1 A supervisor predicts that the number of phone calls at his call center follow a Poisson distribution with mean 4.7 calls per minute. His boss asks him to take 100 samples and confirm his belief. Here is the data: is the supervisor right? Number of Phone Calls per minute 1 or less 2 3 4 5 6 7 8 9 or more 5 7 12 21 10 10 12 10 13 9 9 / 2 6 / 1 5
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EXAMPLE 1 H 0 : Data comes from a Poisson with mean 4.7 H A : Data has a different underlying distribution α=0.1 10 9 / 2 6 / 1 5
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EXAMPLE 1 Number of Phone Calls Per Minute (x) p(x) given μ=4.7 Expected Number (n=100) Observed Number 1 or less 0.0518 5.18 5 2 0.1005 10.05 7 3 0.1574 15.74 12 4 0.1849 18.49 21 5 0.1738 17.38 10 6 0.1362 13.62 10 7 0.0914 9.14 12 8 0.0537 5.37 10 9 or more 0.0503 5.03 13 11 9 / 2 6 / 1 5
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EXAMPLE 1 Reject H 0 12 9 / 2 6 / 1 5 36 . 13 77 . 23 ) ( ) ( 2 1 . 0 2 9 1 2 2 1 2 2 i i i i k i i i i E E f = E E f =
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FORECASTING 13 9 / 2 6 / 1 5
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QUANTITATIVE FORECASTING A statistical technique for making projections about the future using numerical facts and prior experience to predict future events EXAMPLES Sales forecasts Financial projections Assessing future risk and returns 14 9 / 2 6 / 1 5
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REVIEW: EQUATION OF A LINE y = mx + b m = slope of the line b = intercept of the line = point where x = 0 15 9 / 2 6 / 1 5
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EXAMPLE 2 A new company is trying to figure out how much $$$ to spend in advertising.
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