Using housing data, I will try to predict housing prices using a regression model. There are many potential use cases for forecasting housing prices. A real-estate professional may be interested in forecasting revenue. A homeowner may be interested in identifying important features that affect sales price so that they can make appropriate renovation decisions before selling. In any case, my hypothesis is that the specific housing features I collect, such as square footage, bedrooms, etc, are predictive of future housing prices.

In this project, I will follow the steps of The OSEMN framework, i.e. Obtain Scrub Explore Model iNterpret - OSEMN as follows:

The data for this project comes from Kaggle’s House Prices Dataset. The dataset consists of 21597 houses and 21 columns. Each column contains feature, both qualitative and quantitative, that characterize a housing property. The price column is the target variable.

waterfront, view, and yr_renovated have missing values. Also, date and sqft_basement are string objects. Checking the percentage of null values in each of the 3 columns is good way to decide how to deal with null values. If the percentage is high, dropping the column will be a good approach. If the percentage is low , either dropping the rows, binning the columns or replacing the null values with each columns median, mean or mode.

To get rid of outliers, I looked at it through plots and quantile, and I defined a function using scipy library which considers the z-value(number of sigma) = 3 as threshold and returns True if z>3, which means these values are outliers, and return False if z<3, which means these values are not outliers. I used the function to confirm the outlier removal.

Looking at bathroom plot and using my scipy function of outlier removal, bathroom<=4, was the best choice.

Area of the interior living space which is' sqft_living' is linearly correlated with the sale price. Prices rise as sqft of living space increase.

While modelling, we see that the grade of a house, Sqaure foot area of a house, Zipcode and number of bathrooms have large positive coefficients which indicate the effect they have on the pricing of a house. We removed outliers,then ran statsmodels and scikit-learn model and remove variables which have p>0.05 using stepwise method. We again ran statsmodels and scikit-learn model and get R2 score of 0.67 When checking for Normality, the QQ plot looks good. The Homoscedasticity graph looks quite appropriate. We also checked for Multicollinearity, and see that the vif values were all under 5. We Scaled the continous predictors and onehot encoding the categorical variables,then we ran model2 with statsmodels and scikit-learn, and the R2 score increases to 0.82

Hence we will go with Model2. We then validated model2 with cross validation at kfols=5,10,and 20 and got mean square error(MSE) scoring results of all above kfolds similar to each other and similar to the mean square error of training and testing.

To check if the residuals are normally distributed, a Q-Q plot is a helpful visual for analyzing this.

The predicted values of the baseline model are equally scattered which means Homoscedasticity Assumption is maintained, and my baseline model is valid.

The assumption of constant variance appears to be satisfactory maintained

The positive coefficient of the model provides the expected change in the dependent variable (sale price) for a one-unit increase in the independent variable A positive coefficient indicates a positive relationship. As the independent variable increases, the sale price increases. While the negative coffient tells us that the sale price decreases as the independent variable decreases, but with keeping all other variables constant.

1- What are the most powerful features to predict the house sale price of King County?

2- What are the top 10 best zip codes in King County, with regards to the housing sale price?

3- What are the top 10 worst zip codes in King County, considering the housing sale price?

4- What is the most important factor of house sale price in King County?

5- Are the houses overlooking waterfront more expensive?

The following can be inferred from my model: Every unit increase in Square feet living,Square feet lot, Square feet lot 15, and Bathrooms will increase the predicted price.

Predicted price slightly decreases with unit increase in Bedrooms.

The predicted price will increase with increase in latitude as the location moves from South to North.

Predicted price is high for houses with waterfront.

Predicted price is high for houses with condition 4 or 5, and grade greater than 8 and with View.

Predicted price decreases with unit increase in age of house i.e. the year built.

Predicting house prices is quite complex and challenging because it depends on various factors such as Sqft living, No. of bathrooms, grade of a house and Zipcode. The other factors that influence the price are renovation and Waterfront feature.

Finally,our results indicate that in order to provide accurate predictions of house prices, a very large number of features must be used and that they most likely need to be combined with a powerful,complex and non-linear model.