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. These data are also contained in the Arc file Used-car.lsp.

Variable / Info / Description
asking / response / Asking price for a used car.
year / Predictor / 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 (35 points)

  • Fitting base model, critiquing it, and discussing any deficiencies. (5 pts.)
  • Model development, documentation, and discussion. (20 pts.)

Consideration of assumptions

Possible predictor transformations

Stepwise procedures

  • Fitting final model, critiquing it, interpreting it, and discussing any deficiencies.
    (10 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 / 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 Bostonworking.lspfile for Arc, but I would like you fit your final model from Arc using R. Include diagnostic plots for your final model from R.

Grading rubric (35 points)

  • Fitting base model, critiquing it, and discussing any deficiencies. (5 pts.)
  • Model development, documentation, and discussion. (20 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 – Manpower and workload for u.s. navy bachelor officers’ quarters (boq)

The U.S. Navy attempts to develop equations for estimation of manpower needs for manning installations such as Bachelor Officers’ Quarters. Develop such an equation for the U.S. Navy using the dataframeBOQ in R and BOQ.lsp in Arc.

Variable / Info / Description
BERTH
berth / Predictors / Operational berthing capacity
CHECKINS
chkin / Monthly average number of check-ins
COMMONS
commons / Square feet of common use area
OCCUPANCY
occ / Average daily occupancy
ROOMS
rooms / Number of rooms
SERVICE
serv / Weekly hours of service desk operation
WING.NUM
wing / Number of building wings
MANHRS
manhrs / Response / Monthly man-hours, i.e. manpower

Grading rubric (35 points)

  • Fitting base model, critiquing it, and discussing any deficiencies. (5 pts.)
  • Model development, documentation, and discussion. (20 pts.)

Consideration of assumptions

Possible predictor transformations

Stepwise procedures

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

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