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Info3010, week 13 notes

by: Rebecca Evans

Info3010, week 13 notes Info3010

Marketplace > Tulane University > Business > Info3010 > Info3010 week 13 notes
Rebecca Evans
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Notes on normal distributions, simulation trials, predictive modeling, and linear regressions
Business Modeling
Srinivas Krishnamoorthy
Class Notes
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This 4 page Class Notes was uploaded by Rebecca Evans on Monday April 11, 2016. The Class Notes belongs to Info3010 at Tulane University taught by Srinivas Krishnamoorthy in Spring 2016. Since its upload, it has received 14 views. For similar materials see Business Modeling in Business at Tulane University.


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Date Created: 04/11/16
April 4thNotes Dwayne’s Concrete Service Dwayne’s Concrete Service does 10 jobs each month. The probability that a specific job will be for a residential driveway is 70% and the probability that it will be for a commercial project is 30%. Revenues for residential driveways follow a normal distribution with a mean of $500 and a standard deviation of $50. Commercials projects, although more lucrative, also have larger variability. Dwayne estimates revenues here follow a normal distribution with a mean of $1500 and a standard deviation of $400. Set up a model to calculate the average value of revenue each month. 0 0.7 1 Residential commercial 70% 30%  Residential? =if(rand()<0.7, 1, 0)  Residential revenue: residential? Cell*norm.inv(rand(), o Norm.inv function o Know percentage and find corresponding x value o Norm.inv(probability, mean, standard deviation)  Commercial revenue =(1-residential? cell)*norm.inv(rand(), commercial rev mean, commercial rev standard deviation)  Lock cells F4  Logic check if there is residential revenue then commercial revenue is 0 and vice-versa  Simulate 1,00 trials o Link upper right corner of table to the revenue you want to simulate (the total revenue) o Link tells excel what the output we want simulated is o Select entire tabledatawhat-if analysisdata tableleave row input blank and choose random cell for column input  To summarize possible future outcomes: mean and standar deviation o Mean =average(simulation trials) (generally don’t include upper right hand cell but doesn’t matter too much) o Standard deviation =stdev(simulation trials) Thumbs Up Inc. Ian and Sam, the co-founders of Thumbs Up Inc., are planning to build a 300 seat theatre next to Audubon Park. After studying the market, they have drawn the following conclusions:  There will be one show every day  The theatre will make a revenue of $2.00 on each occupied seat; there will be no revenue  from unoccupied seats  The probability that it rains on any given day is 0.30  The demand for seats on a dry day is normally distributed with a mean of 275 and a standard deviation of 30  The demand for seats on a rainy day is normally distributed with a mean of 250 and a  standard deviation of 45 Develop a simulation model to estimate the probability that daily revenue will be below $450.  Rain? =if(rand()<0.3,1,0)  1=rainy day 0=dry day  Daily demand o =IF(B12=1,NORM.INV(RAND(),C3,C4),NORM.INV(RAND(),C5,C6)) o If(rainy, demand given random probability for rainy day, if not demand given random probability for dry day) o Find number on x-axis of normal distribution from a randomly generated probability and the number represents the demand (x-axis) 0 0.3 1 Rainy Dry Norm dist w/ mean 250 Norm dist with mean of 275  Daily revenue o Multiply revenue per seat times number of seats o For number of seats use lower of demand or capacity o =C8*MIN(C12,C7) or =C8*IF(C12<C7,C12,C7)  Simulation trials o To help business plan for future o What ifdata tableblank row and random cell for column  P(daily revenue < $450) o Use count if function o =COUNTIF(C19:C1018,"<450")/1000 o Or /count(C19:C1018) which counts the number of trials  Other method for p(daily revenue)= < 450) o Can do w/ norm. dist fuction =NORM.DIST(450,AVERAGE(C20:C1018),STDEV(C19:C1018), 1) o Find shaded area (probability) that daily revenue is greater than 450 and use average and standard deviation functions o Will be slightly skewed because there is a capacity limit makes it not normally distributed th April 6 Notes Predictive Modeling Linear regression  Analytical tool for: o Relationship b/w variable o Prediction about variable  Example: o Want to predict a theater show’s revenue for the next week o Intuition: look at data from previous week’s revenue o Scatter plot (this example plot gross $ and previous week’s gross $)positive slope line=positive correlation (if a show did well last week-it will do well in future weeks) o Find line of best fit in the scatter plot  Interpreting regression equation o Gross revenue=intercept + slope*previous week’s gross revenue  Slope: x increases then y increases by slope*x amount (ex. Slope=0.96 then an increase in x leads to a smaller increase in y (bc slope less than 1))  Intercept: no real business meaning, when previous week’s gross revenue is $0, place to start line on y-axis Regression in Excel  =SLOPE(y values, x values)  =INTERCEPT(y values, x values)  Using data/data analysis/regression option  Srini quote of the day “getting laid like a rock-star” Final Exam:  Probabilistic modeling o Decision tree, norm distribution, monte carlo simulation  Predictive modeling o Linear regression  Open book exam Expanding predictive modeling models  Expanding Broadway model o Other factors that influence gross $  Holiday week v non-holiday week o Predict opening week?  Play v. musical  Star v. no-star o Err2r in opening week prediction is high for linear regression (r =14%) 2 R  R = variation in the predicted variable explained by our model/total variation in the predicted variable  It measures “goodness of fit” o Tells us how well line fits data on the scatter chart  Extreme scenarios: o R =1: perfect fit, every point falls on line of best fit o R =0: no relations ship, the line of best fit is horizontal to x-axis and points are randomly scatter around it o R values range from 0-1 or as a % from 0-100% o Good R is high, but often is not in business (but at least some of the variation is being explained)


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