Data 605 - Discussion Board
Leticia Salazar
4/13/2022
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Multiple Regression
Real estate price prediction: This real estate dataset was built for regression analysis, linear regression, multiple regression, and prediction models. It includes the date of purchase, house age, location, distance to nearest MRT station, and house price of unit area.
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Data set was obtained through https://www.kaggle.com/datasets/quantbruce/real-estate-price-prediction
# Load Libraries
library(tidyverse)\(~\)
# Import data
real_estate <- read.csv("https://raw.githubusercontent.com/letisalba/Data-605/main/Week-12/Real_estate.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 43.1There are no missing values in this dataset.
# 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 FALSEThis data is complied of 414 rows and 8 columns.
# Glimpse of data set
glimpse(real_estate)## Rows: 414
## Columns: 8
## $ No <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …
## $ X1.transaction.date <dbl> 2012.917, 2012.917, 2013.583, 2…
## $ X2.house.age <dbl> 32.0, 19.5, 13.3, 13.3, 5.0, 7.…
## $ X3.distance.to.the.nearest.MRT.station <dbl> 84.87882, 306.59470, 561.98450,…
## $ X4.number.of.convenience.stores <int> 10, 9, 5, 5, 5, 3, 7, 6, 1, 3, …
## $ X5.latitude <dbl> 24.98298, 24.98034, 24.98746, 2…
## $ X6.longitude <dbl> 121.5402, 121.5395, 121.5439, 1…
## $ Y.house.price.of.unit.area <dbl> 37.9, 42.2, 47.3, 54.8, 43.1, 3…# 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
First I conducted a singluar linear model with House_Price and House_Age. Based on the summary the multiple \(R^2\) is 0.4434 which explains 44.34% variance of the data model 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-05Working with multiple regressions I created another model, this time adding on more cofficients to check how different the two models would be. You can already see some differences with the residuals, the coefficients and the multiple \(R^2\) is now 58.24% and the p-value < 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-16We can see that Longitude has a p-value greater than 0.05 so I will remove it to creat a third regression model. Notice the slight changes in the coefficient values below, 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-16\(~\)
Residual 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)
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# 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')