Introduction
- Housing attributes are influential on price and demand
- Help potential buyers, sellers, and investors
- This data set covers several attributes like bedroom count, net square meters, center distance, metro distance, floor number, age
Method - Multiple Linear Regression
Step 1: Install and load required libraries
#install.packages("ggplot2")
#install.packages("gclus")
#install.packages("ggpubr")
#install.packages("tidyverse")
library(ggplot2) #Used for visualization
library(gclus) #allows us to create a scatterplot
## Loading required package: cluster
library(ggpubr) #Helps us create results that are publication ready
library(tidyverse) #For data manipulation and visualization
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ lubridate 1.9.3 ✔ tibble 3.2.1
## ✔ purrr 1.0.2 ✔ tidyr 1.3.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(readxl) #Helps us to read the excel file
theme_set(theme_pubr()) #gives a clear plot that we can use
Step 2: Import the data
housing_data <- read_excel("/Users/allysonguan/Downloads/house.xlsx")
Step 3: Descriptive Statistics
summary(housing_data)
## bedroom_count net_sqm center_distance metro_distance
## Min. : 1.000 Min. : 10.24 Min. : 11.8 Min. : 1.245
## 1st Qu.: 2.000 1st Qu.: 52.24 1st Qu.: 635.9 1st Qu.: 56.157
## Median : 3.000 Median : 91.83 Median :1143.1 Median :101.388
## Mean : 3.733 Mean :118.94 Mean :1090.5 Mean :105.665
## 3rd Qu.: 5.000 3rd Qu.:150.99 3rd Qu.:1554.3 3rd Qu.:148.481
## Max. :17.000 Max. :750.97 Max. :1999.8 Max. :330.275
## floor age_of_house price
## Min. : 1.000 Min. : 0.00 Min. : 86114
## 1st Qu.: 2.000 1st Qu.:25.00 1st Qu.: 92934
## Median : 8.000 Median :48.00 Median : 95338
## Mean : 9.397 Mean :48.58 Mean : 95701
## 3rd Qu.:16.000 3rd Qu.:72.00 3rd Qu.: 97981
## Max. :24.000 Max. :97.00 Max. :118135
Define Variables-
Independent variables: bedroom count, net sq. meters, center distance (km), metro distance (km), floor, age of house (years)
Dependent variable: Price ($)
Step 4: Data Visualization
#Scatterplot Matrix
pairs( ~ bedroom_count + net_sqm + center_distance + metro_distance + floor + age_of_house + price, data = housing_data)
Step 5: Create the Estimated Regression Model
model <- lm(price ~ bedroom_count + net_sqm + center_distance + metro_distance + floor + age_of_house, data = housing_data)
summary(model)
##
## Call:
## lm(formula = price ~ bedroom_count + net_sqm + center_distance +
## metro_distance + floor + age_of_house, data = housing_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15781.7 -1120.4 56.3 1205.5 13785.8
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.460e+04 1.300e+02 727.77 <2e-16 ***
## bedroom_count 3.086e+02 2.102e+01 14.68 <2e-16 ***
## net_sqm 2.520e+01 5.049e-01 49.91 <2e-16 ***
## center_distance -3.361e+00 7.015e-02 -47.91 <2e-16 ***
## metro_distance 6.998e+00 6.415e-01 10.91 <2e-16 ***
## floor 1.217e+02 4.989e+00 24.39 <2e-16 ***
## age_of_house -2.613e+01 1.149e+00 -22.74 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2079 on 4301 degrees of freedom
## Multiple R-squared: 0.7191, Adjusted R-squared: 0.7187
## F-statistic: 1835 on 6 and 4301 DF, p-value: < 2.2e-16
Estimated Regression Model: ŷ = 94603.76 + 308.57*bedroom + 25.20*net_sqm - 3.36*center_distance + 7.0*metro_distance + 121.66*floor - 26.13*age_of_house
Coefficient Interpretation:
b0- The starting value, “baseline”
b1- Each additional bedroom would increase the price by $308.57
b2- Price increases by $25.20 for each additional square meter
b3- For each additional kilometer from the city center, the price decreases by $3.36
b4- For each additional kilometer from the metro, the price would increase by $7
b5- Each level up, results in an increase by $121.66
b6- For each additional year the house increases in age, the price would decrease by $26.13
Model Interpretation:
- Adj R-squared is average
- Model is significant (p-value < 0.05)
- All the independent variables are significant (p-value < 0.05)
Step 6: Calculate the Correlation Matrix
corr <- cor(housing_data)
rounded_correlations <- round(corr, 2) #Round results to two decimal places
print(rounded_correlations)
## bedroom_count net_sqm center_distance metro_distance floor
## bedroom_count 1.00 0.75 -0.01 0.02 -0.53
## net_sqm 0.75 1.00 -0.01 0.03 -0.41
## center_distance -0.01 -0.01 1.00 0.58 0.02
## metro_distance 0.02 0.03 0.58 1.00 0.00
## floor -0.53 -0.41 0.02 0.00 1.00
## age_of_house -0.06 -0.05 0.01 0.01 0.02
## price 0.55 0.68 -0.42 -0.15 -0.14
## age_of_house price
## bedroom_count -0.06 0.55
## net_sqm -0.05 0.68
## center_distance 0.01 -0.42
## metro_distance 0.01 -0.15
## floor 0.02 -0.14
## age_of_house 1.00 -0.23
## price -0.23 1.00
Interpretation:
bedroom_count (0.55): A moderatly strong correlation, having more bedrooms mean a higer price
net_sqm (0.68): A strong correlation meaning that larger house would sell within a higher rate (net_sqm vs price)
center_distance (-0.42): A moderatly negative correlation showing that houses that are further from the city center tend to cost a bit less
metro_distance (-0.15): A weak negative correlation indicating that proximity to a metro station has only a slight effect on increasing house prices.
floor (-0.14): A weak correlation implying properties on higher floors do not correlate with higher prices
age_of_house (-0.23): A moderatly negative correlation showing older houses might sell less than newer ones, however the relationship isn't very strong
Step 7: Residual analysis
layout(matrix(c(1,2,3,4), 2,2))
plot(model)
Interpretation:
The clustering of residual points near the red line indicate that the model’s prediction are close to the actual values.
Normal Q-Q Plot mostly aligns with the diagonal line, which would indicate that the residuals are normally distributed. The funnel shape suggests a variability of our errors change with the level of the house prices we predict--more variables when prices increase.