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Study Questions for the QM222 TestPart I: Some Thought Questions The vast majority of hotel guests do not take the time to rate their hotel experience on . What sort of bias do you think this might induce in Tripadvisor’s hotel ratings and in what direction (positive or negative)? Explain why.A study finds companies that engage in management practices that are conventionally viewed as risky, such as mandating the use of interdisciplinary teams, tend to perform better than companies that don’t. The study concludes that risky practices improve firm performance in that industry. Describe how survivor bias could have been responsible for the findings.Part II.Here is a correlation table from data on US News’ 2004 rankings of MBA programs and various variables about each program in the “MBA programs” tab.?04 Ave. GMAT04 Acceptance RateAve. Salary & Bonus (Dec.2010 prices)04 Employment at Graduation04 Ave. GMAT104 Acceptance Rate-0.79506341Ave. Salary & Bonus 0.79725018-0.576677628104 Employment at Graduation0.48986355-0.5143419910.4425785581What is the correlation coefficient between GMAT score and acceptance rate? In 1-2 sentences, describe what this correlation coefficient tells us.A junior statistician examining the correlation table you just made concludes that there is a stronger association between GMAT score and employment than between acceptance rate and employment. He bases this on the fact that the correlation between GMAT score and employment is positive, and the correlation between acceptance rate and employment is negative. What do you think of the statistician’s conclusion? Explain in 1-2 sentences.Here is a regression of salaries on GMAT Scores using Data Analysis.(It is Excel output, but this is the same information as Stata output.)SUMMARY OUTPUTRegression StatisticsMultiple R0.79725R Square0.635608Adjusted R Square0.631321Standard Error10731.03Observations87?CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept-17221121456.71592-8.025965.02E-12-214873-12954904 Ave. GMAT403.38133.1280466312.176422.5E-20337.5135469.2484a. In 1-2 sentences, interpret the coefficient on GMAT Scores: i.e. exactly what do we learn from it?b. What information do you get from both this regression coefficient and the correlation between GMAT and salaries? c. What information do you get from this coefficient that you don’t get from the correlation between GMAT and salaries? Predict Salaries for someone with a GMAT= 680. Part III Fuel EfficiencyThe US has regulations requiring a minimum value for the average MPG of the passenger cars that a manufacturer makes. For SUVs (including light trucks), the regulations are less strict. An environmental group wanted to test whether per pound, SUVs had a worse (lower) MPG. They collected data on 45 vehicles, calculated their MPG per 1000 pounds and used this as the dependent (left hand side) variable. They estimated the following regression: MPG/’000lb = 9.671 - 1.213 SUV (22.65) (-5.99)R2 = .831 adj. R2= .829 SEE = 7.98where SUV is a dummy/indicator variable for SUVs (so SUV=1 if the vehicle is an SUV, and SUV=0 if a passenger car)What is the average MPG/’000lb of SUVs? Of cars? Explain how you know, showing any calculations.If the researcher had made a dummy/indicator variable for "cars" instead of "SUVs," what would the equation be? (Fill in intercept (constant) and coefficient on cars) MPG/’000lb = ___________ + ______________ CARS Show how you arrived at these numbers: Part IV: Brookline Housing Data and Goodness of FitWe have run the following three regression to predict price of Brookline Condos. We have run the following three regression to predict price of Brookline Condos. Here are the regressions and their R-squared. Regression A:Regression StatisticsMultiple R0.86546822R Square0.749Adjusted R Sq0.7488035Standard Error131,746 Observations1085?CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept12934.1249705.7121.332630.18293354-6110.0131978.25Size407.4513337.16665956.853730393.3892421.5134Regression B:Regression StatisticsMultiple R0.66516099R Square0.44243915Adjusted R Sq0.44192432Standard Error 196,372 Observations1085?CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept-41574.56519922.79-2.086780.037141-80666.2-2482.93Rooms116705.4263981.03729.315341.5E-139108894124516.8Regression C:Regression StatisticsMultiple R0.196R Square0.038Adjusted R Sq0.038Standard Error257,887 Observations1085?CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept541,4528,753 61.90524276.4558626.9HighRise-128,72219,573 -6.67.48E-11-167127-90316.8Interpret each the coefficient (in words) that anyone would understand.Regression A:Regression B:Regression C:Which of the three regressions gives the most precise predictions of price? How can you tell? Using the most precise regression, make a prediction of the sale price for a 1500 SqFt, 4-room condo in a high rise building. Without doing any new calculations, circle the correlation that is the highest:Correlation of size and priceCorrelation of rooms and priceCorrelation of high rise location and priceIn 1 sentence, explain how you know the answer:Regression C gives you an estimate of how might higher condo prices in high-rises than elsewhere.What is your estimate of how much higher prices are in high rises? Show the calculations that led to your answer.What is your 68% confidence interval around that estimate? Show the pared to condos with fewer rooms, on average, do condos with more rooms sell for: (circle one)morelessabout the sameIf your answer was “more” or “less”, with what percent confidence did you reject the hypothesis that the sale price was about the same? Your intern collects more data indicating whether each condo featured hardwood floors. She created a new indicator variable that equals 1 if the house has hardwood floors and 0 otherwise. She runs a regression and gets the following result:Sale Price = 425,000 + 200,000*HardwoodFloorsWhat is the average sale price of a home with hardwood floors? Show the calculations that led to your answer.What is the average sale price of a home without hardwood floors? Show the calculations that led to your answer.Imagine that your intern had instead defined the variable to be NoHardwoodFloors and set it equal 1 if the house does not have hardwood floors. She runs a new regression that looks like this:Sale Price = b0 + b1 *NoHardwoodFloors What is the value of b0 in the new regression? ______________ What is the value of b1 in the new regression? ______________Show calculations that explain how you derived these answers:Part V. Movies You have collected data on 1832 movies released in the United States between 1995 and 2011. You have information on the following variables:Lifetime GrossThe total gross revenue of the movie made as of May 22, 2013 in millions of 2011 dollarsLifetime TheatersThe total number of theaters the movie is shown as of May 22, 2013YearThe year of Date of ReleaseSeasonSeason in which movie was releaseBudgetThe estimated total cost of producing the movie, in millions of 2011 US DollarsMetascoreA numerical score assigned by to the movie, ranging from 1 (worst reviews) to 10 (best reviews).You created indicator/dummy variables for season and then run the following regression: (Some values have been erased from this table.)Regression StatisticsMultiple R0.67R Square0.45Adjusted R Square0.45Standard Error54.97Observations1832.00?CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept-33.674.71-7.140.00-42.91-24.42Metascore0.850.070.00Budget1.080.03Summer9.893.622.730.012.7816.99Fall-5.573.63-1.540.12-12.681.54Winter5.543.821.450.15-1.9513.03Interpret the R2 of the regression.Interpret the coefficient on Budget.What is the t-statistic associated with the coefficient on Budget? (Show your calculations) What does it tell us? Based on the coefficient on Budget, is investing in producing a movie profitable? Explain (based on the table).Interpret the coefficient on Winter. What can we learn from the corresponding p-value?Holding Metascore and Budget constant, during which season should the producer release a movie? Which season should they avoid?A corrupt employee of offers to change the score of a movie from 5 to 8 and asks for 2.7 million dollars to do so. The (also corrupt) producer of the movie says that the amount is completely unreasonable. Do you agree or disagree with the producer’s statement? Explain.Part VI. Omitted Variable Bias Researchers studying the relationship between guns and crime have collected data on the following variables across all states in 1999: Murder rate: Murders per 100,000 population Violent crime rate: violent crimes of per 100,000 population (includes murders, physical assault, etc.) Concealed Carry Law: Dummy equal to 1 if the state has a law allowing people to legally carry concealed handguns.Robbery rate: Robberies per 100,000 populationRegion: Region of the state (Midwest, Northeast, South, and West)(1)(2)Dependent Variable:Murder rate Murder rate Concealed Carry Law-1.3560.099(0.747)(0.563)region=northeast-0.949-1.594(0.885)(0.624)region=south2.8301.341(0.952)(0.698)region=west0.080-0.053(0.954)(0.665)Robbery Rate 0.025(0.004)Intercept5.1792.152(0.641)(0.630)Observations4848Standard errors in parentheses Do states with Concealed Carry Laws have higher or lower robbery crime rates than states without such laws? Explain how you can tell. [Hint: this is a missing-variable bias question.]Circle one:HIGHERLOWERCAN’T TELLEXPLANATION:Part VII.Executives at a major financial company are trying to model which households own stocks. They collected data for a national sample of households from around the country. The data they collected includes:own_stock:whether or not the household owns any stocks.college:whether the most educated person in the household completed collegehighschool:whether the most educated person in the household completed high school but not collegeThey ask you to model who owns stocks, so you run a set of regressions with “own_stock” as the left hand side (Y) variable.You run this regression. Without any statistics terms or jargon, what does the coefficient 0.1296 tell us? (1-2 sentences.)Regression 1:Regression StatisticsMultiple R0.33171R Square0.110032Adjusted R Square0.109733Standard Error0.394304Observations5962?CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept0.1085530.00715115.17914.35E-510.0945330.122572highschool0.1296130.0128910.055681.34E-230.1043450.154881college0.3322120.01225427.10941E-1520.3081880.356235You have data on BMI and age. You have graphed it and it looks like this:You would like to estimate a regression of BMI on age. What regression would you run that could fit this curve? How would you do this in Stata? ................
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