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Real Estate Company Sale Price Study

Adeline Odunjo

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Outline

1.The Problem

2.The Data

3.Data Preparation

4.Baseline Model 1

5.Full Model 2

6.Reduced (Final) Model 3

7.Model Comparison

8.Regression Equation and Prediction

9.Conclusion and Recommendations

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The Problem

Our client wants a better way to understand what key features (or variables) increase the value of a home. By knowing this information, they will have a more accurate way to predict the selling price of homes to increase their revenue.

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The Data

Final Predictors: Living Rooms^(½), Garage Area, External Quality Rank Coded, Kitchen Quality Rank Coded, Masonry Veneer Type Dummy Code (Brick Dummy, Stone Dummy) Garage Cars, Year Built Rank Code, Masonry Veneer Area, Foundation Dummy Code(Poured Concrete Dummy, Cinder Block Dummy, Brick & Tile Dummy)

Target Variable: Sale Price^(1/3)

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Data Preparation: Data Correction

Corrected Misspellings of variable names and observation values
Imputed missing values with an appropriate measure of center
Imputed data input errors with appropriate measures of center
Imputed anomalies by windorizing values to the normally distributed maximum

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Data Preparation- Quantitative Transformation

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Data Preparation- Categorical Transformation

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We performed an ANOVA test on the variables Foundation and Masonry Veneer Type to confirm that the variables are related to the sale price. Finding that they were useful, we dummy-coded Foundation with "Other" as the reference and Masonry Veneer Type with a "None" reference.
The variables Kitchen Quality and External Quality were both transformed quantitatively by rank coding.

Dummy Coding Foundation

Rank Coding Kitchen Quality

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Data Preparation - Creation

Years Built (Binned and Rank Coded)

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Sale Price (Binned and Rank Coded)*

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Data Preparation- Relationship Tests��Correlation Matrix:

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Baseline Model

As stated, Garage cars were our single best independent predictor which is why we chose to create a baseline model using this variable.

We highlighted the Adjusted R square and Standard Error because these statistics will help identify the effectiveness of the model. Our Baseline Adjusted R square is 0.455 meaning that our regression model can explain 45.5% of the variation in the dependent variable Sale Price. We monitored standard error to see if it decreases in the full model, indicating a better working model. The p-value from the ANOVA test shows that Garage Cars is significant in determining the Sale Price.

Our residual plot looks ok for the most part but there are a couple of values that need attending to. The normal probability plot is relatively even above and below the line with a snakelike pattern. Some observations have been flagged that may be influential/problematic

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Full Model

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Reduced Model

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After removing the problematic observations from our data set, our normal probability plot still had a snake like pattern with some residual outliers toward the lower end. We decided not to run another model because this reduced model showed an increase in the adjusted r square and a decrease in the standard error. We also didn’t want to delete too many observations and change the normality of the distribution. Therefore, this is our final cleaned model. All p-values were still less than the 0.05 significance level, so there were no independent variables to remove from our model. We noticed that although most of the independent variables had a p-value of 0, the ones that are closer to 0.05 are the transformed categorical variables that were dummy coded or rank coded, which was expected.

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Model Comparison

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Regression and Prediction

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Predicted Sale Price^(1/3) =45.633+5.984*(Living Rooms^(½))+0.005*(Garage Area)-2.294*(Exter Qual Rank)-2.296*(Kitchen Quality Rank)-1.223*(Brick Dummy)-1.212*(Stone Dummy)+1.413*(Garage Cars)+0.433*(Year Built Rank)+0.141*(Mas Vnr Area)+4.292*(Poured Concrete)+3.765*(Cinder Block)+2.338*(Brick & Tile)

Predicted Sale Price =45.633+5.984*(2.236)+0.005*(548)-2.294*(2)-2.296*(2)-1.223*(1)-1.212*(0)+1.413*(2)+0.433*(4)+0.141*(14)+4.292*(1)+3.765*(0)+2.338*(0)

Actual Sale Price = $208,500

Predicted Sale Price = $240,347.52

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Regression Equation without Dummy Codes

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Predicted Sale Price =45.633+5.984*(Living Rooms^(½))+0.005*(Garage Area)-2.294*(Exter Qual Rank)-2.296*(Kitchen Quality Rank)+1.413*(Garage Cars)+0.433*(Year Built Rank)+0.141*(Mas Vnr Area)

Actual Sale Price = $208,500.00

(Original) Predicted Sale Price = $240,347.52

(New) Without Dummy Code Predicted Sale Price = $206,484.08

Actual Sale Price = $208,500.00

Difference = $31,847.52

Difference = $2,015.92

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Factors with the most significant impact on the sale price of a home: Rank Code for Kitchen Quality, Garage Cars, Year Built (rank Code), Masonry Veneer Area (square root), Masonry Veneer Type Dummy(None Ref), Foundation Dummy (Other Ref), Living Rooms (square root), Garage Area, and External Quality (rank code).

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The company should expect that a home with these key features will increase the house's sales price. By following this more accurate sale price model, the company can expect an increase in its revenue.

Conclusion

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Model Improvements

Data Collection

To improve the effectiveness of the model and account for some current unexplainable variance we should collect more observations and investigate additional variables
Possible variables to include: Community or Home Pool, Community or Home Tennis Court, Distance from School, Walkability of Neighborhood, Distance from shops and businesses

While the current model is performing well, removing the problematic observations identified in the model assessment, and removing the dummy coded variables will most likely improve the explanation and predictability of the model in general for the surveyed houses.

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