STAT 425 – Modern Methods of Data Analysis

Assignment 1 – OLS Regression (105 points)

Problem 1 – Asking Price for USEd Cars

These 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.

Variable / Info / Description
asking / Response / Asking price for a used car.
year / Predictors / Model year
numopt / Number of options
miles / Miles on odometer
pricenew / Price of car new
loanval / Remainder of original
loan amount left to pay
avgretail / Current blue book value

Grading rubric (25 points)

  • Fitting base model, critiquing it, and discussing any deficiencies. (5 pts.)
  • Model development, documentation, and discussion. (15 pts.)

Consideration of assumptions

Possible predictor transformations

Stepwise procedures

  • Fitting final model, critiquing it, interpreting it, and discussing any deficiencies.
    (5 pts.)

Problem 2 – the boston housing data

The 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 Equation

variable / type / definition / source
CMEDV / Dependent Variable (Y) / Median value of homes in thousands of dollars / 1970 U.S. Census
RM / Structural / Average number of rooms / 1970 U.S. Census
AGE / % of units built prior to 1940 / 1970 U.S. Census
B / Neighborhood / Black % of population / 1970 U.S. Census
LSTAT / % of population that is lower socioeconomic status / 1970 U.S. Census
CRIM / Crime rate / FBI (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)
TAX / Property tax rate / Mass. Taxpayers Foundation (1970)
PTRATIO / Pupil-Teacher ratio / Mass. Dept. of Ed (’71-‘72)
CHAS / Dummy variable indicating proximity to Charles River (1 = on river) / 1970 U.S. Census Tract maps
DIS / Accessibility / Weighted distances to major employment centers in area / Schnare dissertation (Unpublished, 1973)
RAD / Index of accessibility to radial highways / MIT Boston Project
NOX / Air Pollution / Nitrogen oxide concentrations (pphm) / TASSIM

Reference

Harrison, 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 dataframeBoston.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.JMPfile 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 assumptions

Possible predictor transformations

Stepwise procedures

  • Fitting 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 area

These data are contained in the TwinCities.csv file on the website. The variable descriptions are below.

Variable / Info / Description
ID / Label / MLS ID Number
Address / Label / Street Address
CITY / Label / Minneapolis, St. Paul, Shoreview,
Woodbury, Maplewood, West St. Paul
STATE / Label / MN (for all)
ZIP / Label / Zip Code
ListPrice / Response (Y) / Current List Price ($)
BEDS / # of Bedrooms
BATHS / # of Bathrooms (can be fractional)
Location / Name of neighborhood or region in the
Twin Cities metro area.
Don’t use forthis assignment!
SQFT / Square footage of home (ft.2)
LotSize / Square footage of lot (ft.2) – missing for several
of the homes in these data.
YearBuilt / Year the home was built, could be used to create
a new variable called Age = 2014 - YearBuilt
ParkingSpots / # of Parking Spots (I assume off-street parking)
HasGarage / Nominal / Garage or No Garage
DOM / Days on the market, number of days the home
has been listed for sale.
BeenReduced / Nominal / Has the price been reduced from the original
listing price. (Y or N)
OriginalList / ------/ Original listing price. Don’t use as a predictor!!!
BeenReduced2 / Has the price been reduced from the original
listing price (Y or N) – this is calculated differently than
the 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.
LastSaleDate / Date / MM/DD/YY of most recent previous sale of the home. Do not use!
LastSaleDiff / ------/ Current List Price – Last Sale Price. Don’t use!
SoldPrev / Nominal / Has the home been sold previously (Y or N), this one should be Ok to use!
LastSalePrice / Price the home sold for the last time it sold. Don’t use!
Realty / Realty company the home is listed with. Don’t use!
Latitude / Latitude (degrees)
Longitude / Longitude (degrees)
ShortSale / Is 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 assumptions

Possible predictor transformations

Stepwise procedures

  • Fitting final model, critiquing it, interpreting it, and discussing any deficiencies.
    (5 pts.)

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