Data Analytics for Finance (Assignment)
1. Summary of the Process of Analysis
The task is determining how several factors (explanatory/independent variables) affect a house price (dependent
variable). The hypothesis is that house price can be predicted by the 15 presented factors such as lotSize, age, etc.
To test this hypothesis, multiple regression analysis was used. My approach was to use the available data to fit a
multiple regression model for the house price (y), given its explanatory variables (x). I used 13 explanatory variables
to make the best guess for the house price with some combination of the variables. Based on the multiple regression
analysis, crucial findings are as follows:
a. Explanatory variables (lotSize, landValue, livingArea, rooms, and bathrooms), dummy variables (waterfront and
centralAir), and a new variable deriving from the variable’s interaction term (fireplaces*livingArea) have a
positive relationship with the house price.
b. On the contrary, explanatory variables (fireplaces and bedrooms), dummy variable (newConstruction),
transformed variable (SQRT(Age)), and new variable deriving from the variables interaction term
(lotSize*landValue) have a negative relationship with the house price.
After diagnostics of the model, I performed the analysis, such as omitting outliers from the sample size, transforming
variables, and including interaction terms to build a robust regression model.
2. Multiple Linear Regression Analysis
a. Exploratory Data Analysis (EDA)
- By exploring all the datasets, there were some categorical variables (heating, fuel, sewer, waterfront,
newConstruction, and centralAir). These variables were treated as numerical, creating new variables based
on the original variables. For example, waterfront is a yes/no variable indicating the presence of waterfront
in the house, and the new coding for waterfront is 1/0. In another example, the heating variable is
transformed into three dummy variables, which are heating_electric, heating_hotair, and heating_hotwater,
and the new coding for them is 1/0.
Figure 1.1-1.4. Scatterplots of several explanatory variables
• The outliers
By observing all the 1,728 observations, I
cleaned the data by removing some outliers.
Using the graphical EDA, specifically
scatterplots for variables such as lotSize,
landValue, Age, and livingArea as the x-axis
against the house prices as the y-axis (as
seen in Figure 1.1-1.4), it was found 18
outliers. Some outliers were also confirmed
to be outliers using the numerical EDA by
calculating the IQR for the house prices. The
total observations became 1,710.
- Based on the correlation analysis, few variables show a strong relationship with house price. livingArea
(0.71), landValue (0.56), bathrooms (0.60), and rooms (0.53) are highly correlated with house prices.
However, rooms, bedrooms, bathrooms, and livingArea are correlated to each other.
b. Multiple Regression
- I tried to run the first multiple regression using all the explanatory variables. I investigated that some
variables such as age, pctCollege, sewer, fireplaces, heating, and fuel have significant P-values (> 0.05) and
concluded that these variables could be statistically insignificant in the linear relationship with price, and
thus eliminated some of them (pctCollege, sewer, heating, and fuel). However, some variables were
significantly related to the price, specifically age and fireplaces.
- As age and fireplaces are believed to have a significant relationship with the price, I transformed age to
SQRT(Age) using the square root function. This transformation helped make the relationship more linear and
improved the model’s fit. For fireplaces, I investigated that the livingArea interacts with fireplaces. Therefore,
I created an interaction term between livingArea and fireplaces. As both variables are positively correlated,
more fireplaces indicate a bigger house.
- I performed the multiple regression analysis again. The final model's overall regression was statistically
significant (𝑅2 = 0.65), and all the explanatory variables significantly predicted the house price (P-value of all
the variables < 0.05).
