Problem 1 – Asking Price for USEd Cars



STAT 425 – Modern Methods of Data AnalysisAssignment 1 – OLS Regression (105 points)Problem 1 – Asking Price for USEd CarsThese data come from a study of the asking price for different makes and models of cars on the used car market. The response of interest is asking price and the remaining variables are potential predictors. The dataframes to use in R are called Usedcars.working and Usedcars, which includes the make model information for these cars. For developing OLS regression models it will be easier to use the Usedcars.working data frame which you will probably want to rename. These data are also in the file Usedcars.JMP linked to the website.VariableInfoDescriptionaskingResponseAsking price for a used car.yearPredictorsModel yearnumoptNumber of optionsmilesMiles on odometerpricenewPrice of car newloanvalRemainder of originalloan amount left to payavgretailCurrent blue book valueGrading rubric (25 points)Fitting base model, critiquing it, and discussing any deficiencies. (5 pts.)Model development, documentation, and discussion. (15 pts.)Consideration of assumptionsPossible predictor transformationsStepwise proceduresFitting final model, critiquing it, interpreting it, and discussing any deficiencies. (5 pts.)Problem 2 – the boston housing dataThe Boston Housing data set was the basis for a 1978 paper by Harrison and Rubinfeld, which discussed approaches for using housing market data to estimate the willingness to pay for clean air. The authors employed a hedonic price model, based on the premise that the price of the property is determined by structural attributes (such as size, age, condition) as well as neighborhood attributes (such as crime rate, accessibility, environmental factors). This type of approach is often used to quantify the effects of environmental factors that affect the price of a property.Data were gathered for 506 census tracts in the Boston Standard Metropolitan Statistical Area (SMSA) in 1970, collected from a number of sources including the 1970 US Census and the Boston Metropolitan Area Planning Committee. The variables used to develop the Harrison Rubinfeld housing value equation are listed in the table below. (Boston.working)Variables Used in the Harrison-Rubinfeld Housing Value Equationvariable typedefinitionsourceCMEDVDependent Variable (Y)Median value of homes in thousands of dollars1970 U.S. CensusRMStructuralAverage number of rooms1970 U.S. CensusAGE% of units built prior to 19401970 U.S. CensusBNeighborhoodBlack % of population1970 U.S. CensusLSTAT% of population that is lower socioeconomic status1970 U.S. CensusCRIMCrime rateFBI (1970)ZN% of residential land zoned for lots > than 25,000 sq. ft.Metro Area Planning Commission (1972)INDUS% of non-retail business acres (proxy for industry)Mass. Dept. of Commerce & Development (1965)TAXProperty tax rateMass. Taxpayers Foundation (1970)PTRATIOPupil-Teacher ratioMass. Dept. of Ed (’71-‘72)CHASDummy variable indicating proximity to Charles River (1 = on river)1970 U.S. Census Tract mapsDISAccessibilityWeighted distances to major employment centers in areaSchnare dissertation (Unpublished, 1973)RADIndex of accessibility to radial highwaysMIT Boston ProjectNOXAir PollutionNitrogen oxide concentrations (pphm)TASSIMReferenceHarrison, D., and Rubinfeld, D. L., “Hedonic Housing Prices and the Demand for Clean Air,” Journal of Environmental Economics and Management, 5 (1978), 81-102.Develop a regression model for the CMEDV using the available predictors in the table above. In R use the dataframe Boston.working as that will allow you fit the first model using the command:> bos.lm = lm(CMEDV~.,data=Boston.working)As the authors of the original paper were primarily interested in the roll of air pollution in housing prices that variable should be retained throughout. Your analysis should be thorough! Document the model development process by copying and pasting relevant R commands, output, and graphics into your write-up. You may also use the Boston.JMP file linked to the website, but I would like you fit your final model from Arc using R. Include diagnostic plots for your final model from R. Grading rubric (30 points)Fitting base model, critiquing it, and discussing any deficiencies. (5 pts.)Model development, documentation, and discussion. (15 pts.)Consideration of assumptionsPossible predictor transformationsStepwise proceduresFitting final model, critiquing it, and discussing any deficiencies. (5 pts.)Discussion of the role of NOx in your final model, which was the predictor of primary interest to researchers. (5 pts.)Problem 3 – listing Price of homes in the twin cities metro areaThese data are contained in the TwinCities.csv file on the website. The variable descriptions are below.VariableInfoDescriptionIDLabelMLS ID NumberAddressLabelStreet AddressCITYLabelMinneapolis, St. Paul, Shoreview,Woodbury, Maplewood, West St. Paul STATELabelMN (for all)ZIPLabelZip CodeListPriceResponse (Y)Current List Price ($)BEDS# of BedroomsBATHS# of Bathrooms (can be fractional)LocationName of neighborhood or region in theTwin Cities metro area. Don’t use for this assignment!SQFTSquare footage of home (ft.2)LotSizeSquare footage of lot (ft.2) – missing for severalof the homes in these data.YearBuiltYear the home was built, could be used to createa new variable called Age = 2014 - YearBuiltParkingSpots# of Parking Spots (I assume off-street parking)HasGarageNominalGarage or No Garage DOMDays on the market, number of days the home has been listed for sale.BeenReducedNominalHas the price been reduced from the originallisting price. (Y or N)OriginalList-------Original listing price. Don’t use as a predictor!!!BeenReduced2Has the price been reduced from the originallisting price (Y or N) – this is calculated differently thanthe one above. Use one or the other BUT NOT both!ReductAmt-------Amount of the reduction from the original listing price if it has been reduced. Don’t use as a predictor!!!PerReduct-------Percent reduction from the original listing price. I wouldn’t use this predictor either, but in might be Ok to use.LastSaleDateDateMM/DD/YY of most recent previous sale of the home. Do not use!LastSaleDiff---------Current List Price – Last Sale Price. Don’t use!SoldPrevNominalHas the home been sold previously (Y or N), this one should be Ok to use!LastSalePricePrice the home sold for the last time it sold. Don’t use!RealtyRealty company the home is listed with. Don’t use!LatitudeLatitude (degrees)LongitudeLongitude (degrees)ShortSaleIs more money owed on the home than what the asking price is? (Y or N)Grading rubric (35 points)Fitting base model, critiquing it, and discussing any deficiencies. (5 pts.)Model development, documentation, and discussion. (15 pts.)Consideration of assumptionsPossible predictor transformationsStepwise proceduresFitting final model, critiquing it, interpreting it, and discussing any deficiencies. (5 pts.) ................
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