With the ongoing pandemic of COVID-19, interest rates for mortgages have dropped which opens up many financial opportunities for people to buy homes. According to Forbes, "buyers are currently outnumbering sellers [and] with so much demand and a low inventory, [seller]s are bound to make a quick sale and a higher profit." Now is the time to act quickly to make profits in real estate, and if you're looking into the housing market in King County, WA, save time and maximize profits by searching armed with the information provided below.
There are many factors that can affect a home's overall saleprice: from the individual characteristics of the property to the surrounding community in which the property is located. But there is no single factor that can predict the sales price of a home; rather, it is the combination of the factors. The data displayed in the heatmap below represents all the data gathered for King County's housing data from 2014-2015.
Out of the many factors that play into pricing a home in King County, the natural tiers and distinct patterns of price brackets that are created by the location of the houses seems to be the largest contributing factor to the price of a house. The following factors will be explored through the analysis of the following characteristics in relation to the location of the house:
- Price per Square-Foot
- Distances to Points of Interest
- Population Density
Properties with larger square footages tend to hold a higher value. However, when considering other factors (especially location) square footage alone can't illustrate a concrete trend in housing prices. In order to visualize the trends, square footage of homes will be observed on the basis of longitude and latitude juxtaposed with its prices to obtain a better understanding of the relationship of square footage and house price.
The plot above displays a trend where the concentrations of houses with lower square footage are highest in the west of King County.
Note how the price per squarefoot has a general trend of being the higher in the northern half of King County.
In order to see how proximity to a point of interest affects housing prices, the average housing price within a certain interval will be observed: using 5 mile intervals starting at 0 miles and ending at 30 miles. By looking at the average housing price in each interval, trends will be better displayed.
Houses that are close to the airport have a lower average housing price. This is likely due to the fact that noise from the air traffic negatively impacts the housing price. Houses that are 10 to 20 miles have the highest average price. These houses are probably far away enough from the airport to not be significantly affected by noise but close enough that the commute to the airport is convenient. Average housing price compared to distance to the nearest Link station is not as definitive. Seattle does have an extensive road network and it may be the case that commuting by car is still commonplace enough within Seattle that proximity to a metro station is not the best indicator of housing price.
Locations further away from either the Seattle Center or CenturyLink Field, the average housing price decreases. Houses less than 5 miles from Seattle Center are on average more expensive than houses within 5 miles of CenturyLink Field. This suggests that Seattle Center may be a more popular venue.
Proximity to a greenspace clearly has an effect on average housing price. Discovery Park is the largest park in King County and Kerry Park offers an ideal view of the popular Space Needle and access to water. Those houses that are more than 20 miles from either park are likely to fall within the southern or eastern part of King County.
The scatter plot above shows that houses closer to 4 out of the 5 points of interest we chose (Seattle Center, CenturyLink Field, Kerry Park, and Discovery Park) are more expensive. The houses closest to the airport are less expensive which confirms the results of the bar plot above. Kerry Park, Discovery Park, and Seattle Center seem to be locations where you can expect high housing prices. The scatter plot above is further proof that location is an important factor in determining the price of a home.
Parts of an area can be characterized from metropolitan to rural via population densities, but not all metropolitan areas will always have a higher housing prices in comparison to more rural areas. These trends are observed when viewing the relationship between houses in certain population density tiers and their prices. (Because the data was obtained by zipcode, the information is visualized categorically to avoid the nonlinearity of the relationship.)
Notice in the plot above, how there is a higher volume of houses sold in the more rural areas of King County versus the more metropolitan areas.
The plot above displays (even without outliers) that the price of the average home increases as the density of the population surrounding the area increases. When noting the deviations of each individual column, it also generally increases as the population density increases.
To create a model for predicting the sales price, the original set of variables of the data (shown in the heatmap above) was filtered to narrow down the best predicting variables to use to model the data. First the data was processed to reduce colinearity and multicolinearity via filtration (set by pearson correlation coefficients and VIF scores), creation of interactions and categorical data, diffusion of unbalanced weights created by a small number of categorical features, and removal of outliers determined by standard deviations. Thus the resulting features of the predictors are narrowed down to the variables displayed below.
The heatmap above displays the resulting features that will be used to model housing price data.
After running through cycles of fitting models and condensing data according to the stats describing the goodness of fit, the final model was analyzed via the qqplot below.
The residuals for the model seem to be normally distributed, although the tails of the qqplot imply that there are some more outliers that could be eliminated in order to improve the accuracy of the model.
The final assumption that we will check will be for homoscedasticity. The Breusch-Pagan and the White test results in p-values that are nearly zero. This implies that the data is in fact heteroscedastic and the data does not meet the necessary assumptions to be a linear model.
All of the variables with the exception of dist_to_seattle_center seem to be fairly homoscedastic. The variance in the residuals of dist_to_seattle_center isn't consistent so a linear regression model will not be the most reliable for this dataset.
It may be the case that the data is better modeled with a polynomial regression rather than linear. And after fitting a range of polynomial regressions, the meansqured error of the cross validation score show that the data is best modeled by a second degree polynomial.
Above is the actual versus predicted price for each house based upon the model fitted by a 2nd degree polynomial.
Recommendations:
-
In terms of price per square foot, those with higher budgets should looks towards the northern and western parts of King County for either purchasing or investing. For those with lower budgets or those just entering the housing market, the soutern part of King County is typically more affordable.
-
When considering local attractions or transportation, choose a property within a 5 mile radius from Seattle Center/Kerry Park or Discovery Park. These homes have the highest average price for home within 5 miles. The Link System serves parts of King County with both higher and lower priced homes, however homes within 20 miles of a Link Station tend to have higher values. It should be noted that the Link System only serves the western part of King County so that does impose a restrictions withn buyer interests.
-
When taking into account population density, buyers will have a greater availability of houses if target housing search is in a area with a population density of less than 6400 people per square mile. We suggest starting your housing search in these area due to the high abundance of properties sold. If you have a higher budget or plan on flipping a house, you may want to look at investing in an area where there is a higher population density as those properties tend to sell for a higher price.
Model Performance: Due to outliers having a less than normal distribution as well as both the White and Breusch-Pagan Test indicating a heteroscedastic model, a polynomial regression of degree 2 was the best fit for the data. As a second degree polynomial, the model is approximately 67% accurate with a mean squared error of 0.014.