Data 605 - Discussion Board12
IvanTikhonov
2022-11-09
Multiple Regression
Real estate price prediction:Regression analysis, linear regression, multiple regression, and prediction models were all used to build this real estate dataset. It covers the purchase date, the age of the house, the location, the distance to the closest MRT station, and the housing price per square foot.
Data set was acquired using https://www.kaggle.com/datasets/quantbruce/real-estate-price-prediction
# Load Libraries
library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.2.2## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.3.6 ✔ purrr 0.3.5
## ✔ tibble 3.1.8 ✔ dplyr 1.0.10
## ✔ tidyr 1.2.1 ✔ stringr 1.4.1
## ✔ readr 2.1.3 ✔ forcats 0.5.2## Warning: package 'readr' was built under R version 4.2.2## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()# Import data
real_estate <- read.csv("https://raw.githubusercontent.com/IvanGrozny88/DATA605Assignment_12/main/Real%20estate.csv")
head(real_estate, n = 5)## No X1.transaction.date X2.house.age X3.distance.to.the.nearest.MRT.station
## 1 1 2012.917 32.0 84.87882
## 2 2 2012.917 19.5 306.59470
## 3 3 2013.583 13.3 561.98450
## 4 4 2013.500 13.3 561.98450
## 5 5 2012.833 5.0 390.56840
## X4.number.of.convenience.stores X5.latitude X6.longitude
## 1 10 24.98298 121.5402
## 2 9 24.98034 121.5395
## 3 5 24.98746 121.5439
## 4 5 24.98746 121.5439
## 5 5 24.97937 121.5425
## Y.house.price.of.unit.area
## 1 37.9
## 2 42.2
## 3 47.3
## 4 54.8
## 5 43.1This dataset has no missing values.
# Checking is missing values
head(is.na(real_estate))## No X1.transaction.date X2.house.age
## [1,] FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE
## [3,] FALSE FALSE FALSE
## [4,] FALSE FALSE FALSE
## [5,] FALSE FALSE FALSE
## [6,] FALSE FALSE FALSE
## X3.distance.to.the.nearest.MRT.station X4.number.of.convenience.stores
## [1,] FALSE FALSE
## [2,] FALSE FALSE
## [3,] FALSE FALSE
## [4,] FALSE FALSE
## [5,] FALSE FALSE
## [6,] FALSE FALSE
## X5.latitude X6.longitude Y.house.price.of.unit.area
## [1,] FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE
## [3,] FALSE FALSE FALSE
## [4,] FALSE FALSE FALSE
## [5,] FALSE FALSE FALSE
## [6,] FALSE FALSE FALSEThere are 414 rows and 8 columns in this data set.
# Summary of data set
summary(real_estate)## No X1.transaction.date X2.house.age
## Min. : 1.0 Min. :2013 Min. : 0.000
## 1st Qu.:104.2 1st Qu.:2013 1st Qu.: 9.025
## Median :207.5 Median :2013 Median :16.100
## Mean :207.5 Mean :2013 Mean :17.713
## 3rd Qu.:310.8 3rd Qu.:2013 3rd Qu.:28.150
## Max. :414.0 Max. :2014 Max. :43.800
## X3.distance.to.the.nearest.MRT.station X4.number.of.convenience.stores
## Min. : 23.38 Min. : 0.000
## 1st Qu.: 289.32 1st Qu.: 1.000
## Median : 492.23 Median : 4.000
## Mean :1083.89 Mean : 4.094
## 3rd Qu.:1454.28 3rd Qu.: 6.000
## Max. :6488.02 Max. :10.000
## X5.latitude X6.longitude Y.house.price.of.unit.area
## Min. :24.93 Min. :121.5 Min. : 7.60
## 1st Qu.:24.96 1st Qu.:121.5 1st Qu.: 27.70
## Median :24.97 Median :121.5 Median : 38.45
## Mean :24.97 Mean :121.5 Mean : 37.98
## 3rd Qu.:24.98 3rd Qu.:121.5 3rd Qu.: 46.60
## Max. :25.01 Max. :121.6 Max. :117.50# Getting colnames
colnames(real_estate)## [1] "No"
## [2] "X1.transaction.date"
## [3] "X2.house.age"
## [4] "X3.distance.to.the.nearest.MRT.station"
## [5] "X4.number.of.convenience.stores"
## [6] "X5.latitude"
## [7] "X6.longitude"
## [8] "Y.house.price.of.unit.area"# Renaming for easier read
colnames(real_estate) <- c("No", "Transaction_Date", "House_Age",
"Nearest_MRT_Station", "Number_Convenience_Stores",
"Latitude", "Longitude", "House_Price")
head(real_estate)## No Transaction_Date House_Age Nearest_MRT_Station Number_Convenience_Stores
## 1 1 2012.917 32.0 84.87882 10
## 2 2 2012.917 19.5 306.59470 9
## 3 3 2013.583 13.3 561.98450 5
## 4 4 2013.500 13.3 561.98450 5
## 5 5 2012.833 5.0 390.56840 5
## 6 6 2012.667 7.1 2175.03000 3
## Latitude Longitude House_Price
## 1 24.98298 121.5402 37.9
## 2 24.98034 121.5395 42.2
## 3 24.98746 121.5439 47.3
## 4 24.98746 121.5439 54.8
## 5 24.97937 121.5425 43.1
## 6 24.96305 121.5125 32.1Regression Analysis I started by running a simple linear model using the variables house price and house age. The multiple R2 is 0.4434, which according to the summary explains 44.34% of the data model’s variance, and has a p-value of 1.56e-05, which is less than 0.05.
# Obtaining our singular Linear Model
my_lm <- lm(House_Price ~ House_Age, real_estate)
summary(my_lm)##
## Call:
## lm(formula = House_Price ~ House_Age, data = real_estate)
##
## Residuals:
## Min 1Q Median 3Q Max
## -31.113 -10.738 1.626 8.199 77.781
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 42.43470 1.21098 35.042 < 2e-16 ***
## House_Age -0.25149 0.05752 -4.372 1.56e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.32 on 412 degrees of freedom
## Multiple R-squared: 0.04434, Adjusted R-squared: 0.04202
## F-statistic: 19.11 on 1 and 412 DF, p-value: 1.56e-05Managing various regressions To see how the two models would differ from one another, I developed a second model and this time added extra coefficients. There are already some variations between the multiple, coefficients, and residuals. The current R2 is 58.24%, and the p-value is 2.2e-16.
# Running the multiple regression
my_lm2 <- lm(House_Price ~ Transaction_Date + House_Age +
Nearest_MRT_Station + Number_Convenience_Stores +
Latitude + Longitude, real_estate)
summary(my_lm2)##
## Call:
## lm(formula = House_Price ~ Transaction_Date + House_Age + Nearest_MRT_Station +
## Number_Convenience_Stores + Latitude + Longitude, data = real_estate)
##
## Residuals:
## Min 1Q Median 3Q Max
## -35.664 -5.410 -0.966 4.217 75.193
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.444e+04 6.776e+03 -2.131 0.03371 *
## Transaction_Date 5.146e+00 1.557e+00 3.305 0.00103 **
## House_Age -2.697e-01 3.853e-02 -7.000 1.06e-11 ***
## Nearest_MRT_Station -4.488e-03 7.180e-04 -6.250 1.04e-09 ***
## Number_Convenience_Stores 1.133e+00 1.882e-01 6.023 3.84e-09 ***
## Latitude 2.255e+02 4.457e+01 5.059 6.38e-07 ***
## Longitude -1.242e+01 4.858e+01 -0.256 0.79829
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.858 on 407 degrees of freedom
## Multiple R-squared: 0.5824, Adjusted R-squared: 0.5762
## F-statistic: 94.59 on 6 and 407 DF, p-value: < 2.2e-16Since Longitude has a p-value above 0.05, as can be seen, I will eliminate it to create a third regression model. The coefficient values below show some tiny variations, but they are all less than 0.05.
# Multiple regression without Longitude
my_lm3 <- lm(House_Price ~ Transaction_Date + House_Age + Nearest_MRT_Station +
Number_Convenience_Stores + Latitude, real_estate)
summary(my_lm3)##
## Call:
## lm(formula = House_Price ~ Transaction_Date + House_Age + Nearest_MRT_Station +
## Number_Convenience_Stores + Latitude, data = real_estate)
##
## Residuals:
## Min 1Q Median 3Q Max
## -35.623 -5.371 -1.020 4.244 75.346
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.596e+04 3.233e+03 -4.936 1.17e-06 ***
## Transaction_Date 5.135e+00 1.555e+00 3.303 0.00104 **
## House_Age -2.694e-01 3.847e-02 -7.003 1.04e-11 ***
## Nearest_MRT_Station -4.353e-03 4.899e-04 -8.887 < 2e-16 ***
## Number_Convenience_Stores 1.136e+00 1.876e-01 6.056 3.17e-09 ***
## Latitude 2.269e+02 4.417e+01 5.136 4.36e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.848 on 408 degrees of freedom
## Multiple R-squared: 0.5823, Adjusted R-squared: 0.5772
## F-statistic: 113.8 on 5 and 408 DF, p-value: < 2.2e-16Residual Analysis
# my_lm
par(mfrow = c(2,2))
plot(my_lm)
# my_lm2
par(mfrow = c(2,2))
plot(my_lm2)
# my_lm3
par(mfrow = c(2,2))
plot(my_lm3)
# my_lm
hist(my_lm$residuals, xlab = 'Residuals', main = 'Histogram of Singluar Linear Model')
#my_lm2
hist(my_lm2$residuals, xlab = 'Residuals', main = 'Histogram of Multiple Linear Model')
#my_lm3
hist(my_lm3$residuals, xlab = 'Residuals', main = 'Histogram of Multiple Linear Model without Longitude')
Conclusion: This model does fit the data because residuals are regularly
distributed, particularly for the second and third models that were
developed.