market is one of the largest financial markets in the United States, a model which contributes to price efficiency and discovery is good for the overall economy. Lastly, valuation of mortgaged homes that have not recently sold is an important problem for investors in mortgage backed securities.Our Hypothesis:As discussed before, our design variables chosen are listed below with definitions:grade:overall grade given to the housing unit, based on King County grading systemsqft_living: square footage of the homeyr_built: year of constructionOur hypothesizes were formed as follows:H0: no single variable or interaction variable is predictive of home prices (betas of zero) H1: at least one beta is not zeroFurther, we expect square footage and grade to have a positive relation to home prices and be predictive. Probably the same is true with age, (newer more expensive), but here itis less clear because newer homes are cheaper to build and may be lower quality. Some older homes may demand a premium.
Results of Statistical AnalysisThe house prices we collected are shown below:RunFactorsResponsegradeSqft_livingyr_builtHouse Price($)1+++8500002++-5800003+-+5500004+--7600005-++3999006-+-5745007--+2499008---380000First of all, we generated some plots to get an idea about the data.Plots of the main effects showing the house price for the different categories for each factor:The strong positive correlation between sqft and price drew our attention first. The median, 1stand 3rdquantilesas well as the min and max of bigger house price are remarkably higher than those of smaller-sized houses. In addition, grade seemed to
demonstrate a positive relation with house price, though not as much as the size, but definitely worth further investigation. Last, it’s intriguing that the age of house doesn’t look to be a determinant to the house price. Newer houses have a wider rangeof prices, and some older houses may demand a premium.