Provided by: Ali Mahzoon
King county is considered as 11th largest county in Washington state (slightly larger than 21 million tennis courts). Finding houses in such a large county has always been a problem for people to find a house that is not over price. On the other hand people don't want to spend their money until they are sure they couldn't have found a better place geographically.
we are real-state investors, we can use this model to project prices and to see properties are over or under value.
- Is the house price change based on the location?
- What is the average house price base on the city in this county?
- What is the price of a house with specific features?
- Can people get any recommendation based on their available money? (i.e. I have x money what I can buy)
- Is it possible to predict a house price based on the house features (bedrooms, bathrooms,...)?
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Dataset and Tools:
- Given data by King County House Sales
- statsmodel and scikit learn library
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Approach:
- Feature Engineering
- Multicolinearity of features
- Multiple linear regression
- Model fit in linear regression by using Stepwise selection with p-values, finding interactions by cross validation
- Regression model validation by calculating Root Mean Squared Error (RMSE)
- Data visualized by Seaborn and Matplotlib
We divide the King County map into 4 prats (NW, NE, SW, SE) as we can see most of the high-price houses (houses more than 613,275$) are mostly located at North and a little tendency to East.
On the other hand as we go toward South West houses become less expensive (houses less than 317,000$) as we can see in the following image.
This categorization of data gives us a high level overview of price based on location. Our real-state concentration is on prices raging from 173,000$ to 907,000$ which makes our real-state unique because of helping people to find houses all over the King County with different prices. (it needs to be mentioned that there are houses that are more than 7 million dollar!).
Average prices in different cities (Descending)
We have the information of 21,507 houses in the King county in Washington state, so if people want to know the price of a house in each city or even more accurate in each Zipcode, our real-state can find a similar house in that area and predict the price of the house. The goodness of fit of our model ,R-Squared, after using stepwise selection with p-values and using interactions on our training set is 0.748.
The top 15 coefficients are:
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InterPretation:
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for %1 increase in sqft_living price will be increased by 81$
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we can see the interaction of city_Federal Way and sqft_living results in decrease in price. that's why prices in cities located on the south west are less expensive than the ones located on north east.
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If the house is renovated the price will increase by 18000$
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grade is a feature of a house which is determined by the king county itself. If you want to buy a house with higher grade the house price will increase by 45000$
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The interesting thing is that if you are obsessed with the grade of your house, you can find houses with high grades in South West and you don't need to pay that much money for these houses.
The Root Mean Squared Error (RMSE) which shows how off we can be on our target variable (in this model price). It is an acceptable number to calculate prices of houses around 1MM$ (approximately %10 of the house price) but for houses with prices less tan 500k$ (rmse would be more than %20 of the house price) is not acceptable.
In the following picture you can see the QQ-plot to keep track of residuals.
In statistics, a sequence of random variables is homoscedastic if all its random variables have the same finite variance. we can chceck the homoscedasticity assumption by using a regplot.
Houses located on North east are more expensive than houses located on south west. The most important feature of a house that has linear relationship with price of the house is the size of the house including having a basement, bedrooms, and bathrooms. Construction grade has a slightly linear relationship with price.
If you are looking for a house in cities like Medina, Mercer Island, and Bellevue you probably end up having a house with the price more than 700,000$. However, if you are willing to buy a house in cities like Kent, Auburn, and Federal Way even by spending much less money (less than 300,000) you might even get a bigger house.