Is there a correlation between Property price and distance from CBD in Melbourne
A analysis based on the statistics
Student(s) Names: Sovit BAral and Student ID’s:s3870624
Descriptive Statistics and Visualisation
- The important variable in the analysis are distance from CBD and the property price.
- Summary statistics are calculated for property price and visually displayed.
- Distribution analysis are performed for property price.
- Scatter plot with line fitting are performed to understand if the is a correlation between distance from CBD and propety price.
# URL of the data for reference only if we wish to scrapre from the web
urldata1 <-"https://www.kaggle.com/anthonypino/melbourne-housing-market/download"
#set the working directory to import the excel file for analysis
filename<-setwd("C:/Users/212458752/Desktop/house")
getwd() # confirm if the default directly has been set
## [1] "C:/Users/212458752/Desktop/house"
#****************DATA Preprocessing START***************
#import the data into R from working directory
options(scipen = 999)
house_data<- data.frame(read.csv(file = "C:/Users/212458752/Desktop/house/Melbourne_housing_FULL.csv"))
house_data<- house_data[, c(1,5,9)]# drop all other unnecessary columns
house_data <- house_data[!is.na(house_data$Price),]# omit NAs in property price
house_data <- house_data[!is.na(house_data$Distance),]# omit NAs in distance
house_data$Distance <- as.double(house_data$Distance)# convert distance variable as a factor
str(house_data)
## 'data.frame': 27247 obs. of 3 variables:
## $ Suburb : chr "Abbotsford" "Abbotsford" "Abbotsford" "Abbotsford" ...
## $ Price : int 1480000 1035000 1465000 850000 1600000 941000 1876000 1636000 1000000 745000 ...
## $ Distance: num 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 ...
check_infinite<-sapply(house_data, is.infinite)%>% invisible() # function to Checks if the dataframe has any infite value
is.special <- function(x){
if (is.numeric(x)) (is.infinite(x) | is.nan(x))
}
check_special<-sapply(house_data, is.special)%>% invisible()# call the function
View(house_data)# View the data
#****************DATA Preprocessing End***************
#****************OUtlier Analysis Start***************
boxplot(house_data$Price,outline=TRUE, names ="Outliers analysis on Prices", main="Outliers analysis on Prices ", ylab = "Property Price", xlab = " Box plot")
# From box plot Pricee variable has an outlier.
# further Z score computation need to be performed on Price Data
#Z Score for average price data
z.scores_price <- house_data$Price %>% scores(type = "z")
z.scores_price %>% summary()
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -1.5046 -0.6472 -0.2809 0.0000 0.3817 15.8228
length (which( abs(z.scores_price) >3 ))# number of outliers detected
## [1] 474
outlier<-( which( abs(z.scores_price) >3 ))# Find the location of outlier whose absolute value is greater than 3
house_data<-house_data[-(outlier),]# remove suburbs that has the outliers values
boxplot(house_data$Price,outline=TRUE, names =" Price after Outliers removal", main="Price after outliers removed ", ylab = "Property Price", xlab = " Box plot") # recheck after outliers removal in property price
averprice <- house_data %>% group_by(Suburb) %>% summarise(Average_price_of_Suburb = sum(Price)/n())
# REclassify the property prices to suburb by calculating the mean price os each suburb.
## OUtlier analysis on distance
## Boxplot for distance
boxplot(as.integer( house_data$Distance),outline=TRUE,names ="OUliers analysis on distnce from CBD", main=" Distance from CBD ", ylab = "Distance", xlab = " Box PLot ")
# we are only interested in calculating distance from CBD which are less than 60 Kms from the CBD
house_data$Distance <- ifelse(house_data$Distance > 60, NA,house_data$Distance)# Drop any distance over 60 Kms
# compute the average of the distance. this is not normally necessary but it will help us to match the data points with price
averdist <- house_data %>% group_by(Suburb) %>%
summarise(Average_distance_fromCBD = sum(Distance)/n())
#****************OUtlier Analysis End***************
#****************Data Preprocessing Start****************
# Create a new variable as a data frame to store the price and distance by suburb data.
dist_and_price<- as.data.frame(inner_join(averprice,averdist,by= "Suburb"))# new data frame
dist_and_price <- dist_and_price[!is.na(dist_and_price$Average_price_of_Suburb),]# omit any NAs
dist_and_price <- dist_and_price[!is.na(dist_and_price$Average_distance_fromCBD),]#Omit any NAs
print.data.frame(head(dist_and_price))# to view the crime data as it appear in the excel file
## Suburb Average_price_of_Suburb Average_distance_fromCBD
## 1 Abbotsford 1033549.0 2.700980
## 2 Aberfeldie 1269615.9 8.288406
## 3 Airport West 751364.2 11.898675
## 4 Albanvale 536055.6 14.000000
## 5 Albert Park 1784901.2 3.181395
## 6 Albion 615123.7 12.174627
#****************Data Preprocessing End****************
#****************Summary Statistics Start****************
summary_stat <- data.frame (mean= c(mean(dist_and_price$Average_price_of_Suburb, na.rm = TRUE),mean(dist_and_price$Average_distance_fromCBD, na.rm = TRUE)),
median= c(median(dist_and_price$Average_price_of_Suburb, na.rm = TRUE),median(dist_and_price$Average_distance_fromCBD, na.rm = TRUE)),
stdv = c(sd(dist_and_price$Average_price_of_Suburb, na.rm = TRUE),sd(dist_and_price$Average_distance_fromCBD, na.rm = TRUE)),
maximum= c(max(dist_and_price$Average_price_of_Suburb),max(dist_and_price$Average_distance_fromCBD)),
minimum= c(min(dist_and_price$Average_price_of_Suburb),min(dist_and_price$Average_distance_fromCBD)),
Q1= c(quantile(dist_and_price$Average_price_of_Suburb, probs = 0.25),quantile(dist_and_price$Average_distance_fromCBD, probs = 0.25)),
Q3= c(quantile(dist_and_price$Average_price_of_Suburb, probs = 0.75),quantile(dist_and_price$Average_distance_fromCBD, probs = 0.75)),
IQR= c(IQR(dist_and_price$Average_price_of_Suburb),IQR(dist_and_price$Average_distance_fromCBD)) ) -> table1
knitr::kable(table1)
| 896242.4847 |
839076.7 |
296516.82279 |
1808234.4 |
380000.000000 |
659869.652614 |
1064566.28 |
404696.63109 |
| 17.2836 |
14.8 |
10.46858 |
48.1 |
1.005085 |
9.221416 |
23.05 |
13.82858 |
summary_stat_price<-t(summary_stat[1,])
barplot(summary_stat_price,
main = "Summary Statistics for Average HOuse Prices in Melbourne ",
xlab = " Data Summary ",
ylab = "Property Prices",
col = c("red","green","blue","Yellow","Purple","darkred","black","Orange"),
beside = T,
horiz = FALSE)
legend("topright",
c("Mean","Median","St Dev","Maximum","Minimun", "Q1","Q3", "IQR"),
fill =c("red","green","blue","Yellow","Purple","darkred","black","Orange"))
grid(nx=NA, ny=NULL)
#****************Summary Statistics End****************
#***************Data Fitting Start*********************
# This is a chunk for your Distribution Fitting section.
#Analysis for Male
# PLotting histogram for male pre analysis
Price_plot <- ggplot()
Price_plot <- Price_plot + geom_histogram(aes(x=dist_and_price$Average_price_of_Suburb), bins=100)
Price_plot <- Price_plot + scale_x_continuous(trans='log10')
Price_plot <- Price_plot + labs(x="Average property price", y= "Frequency ")
Price_plot <- Price_plot + geom_vline(xintercept = mean(dist_and_price$Average_price_of_Suburb), size=1.5, colour ="red")
Price_plot <- Price_plot + geom_vline(xintercept = median(dist_and_price$Average_price_of_Suburb), size=1.5, colour ="blue")
#Display the histogram
Price_plot
shapiro.test(dist_and_price$Average_price_of_Suburb)
##
## Shapiro-Wilk normality test
##
## data: dist_and_price$Average_price_of_Suburb
## W = 0.94878, p-value = 0.000000001478
kurtosis(dist_and_price$Average_price_of_Suburb)
## [1] 0.1370957
hist(dist_and_price$Average_price_of_Suburb, freq=F, breaks=12)
lines(density(dist_and_price$Average_price_of_Suburb), col="red")
legend("topright", c("NOrmal Distribution "), fill =c("red","green"))
#***************Data Fitting End*********************
#**************** Correlation analysis Start********************
cor(dist_and_price$Average_price_of_Suburb, dist_and_price$Average_distance_fromCBD)# to calculate correlation coefficient
## [1] -0.4670735
correlation_graph <- ggplot(dist_and_price, aes(x = Average_distance_fromCBD, y = Average_price_of_Suburb)) +
geom_point(aes()) +
stat_smooth(method = "lm",
col = "#C42126",
se = FALSE,
size = 1)
correlation_graph+
scale_x_continuous(breaks = seq(1, 50, by = 2)) +
scale_y_continuous(breaks = seq(300000, 3000000, by = 200000)) +
labs(
x = "Distance from CBD(Kms)",
y = "Property Price($)",
color = "Gear",
title = "Correlation between distance from CBD and property price",
subtitle = "Average sold price of the property",
caption = "There exist a liner relationship"
)
#**************** Correlation analysis End********************
Hypothesis Testing
Assumptions: * The distance and the property price are correlated. * If we know the distance of the property from the CBD we could compute the price. * Independence: Independence was assumed as property prices came from multiple data source. * Linearity: The scatter plot suggested a linear relationship.However all other parameters like land size, property age, sold year were ruled out.
Analysis: * From above analyis it can be seen that there is a liner relationship between distance and price * Property price follow the normal distribution and skewed at the right * We need to compute the statistically significance of the data.
#Hypotheses testing
#Fit a linear regression model to the data and assess the fit to determine if the model statistically significant
options(scipen = 999)# supress scientific notation
Hypotheses_model<-lm( Average_price_of_Suburb~Average_distance_fromCBD , data = dist_and_price )
Hypotheses_model %>% summary()
##
## Call:
## lm(formula = Average_price_of_Suburb ~ Average_distance_fromCBD,
## data = dist_and_price)
##
## Residuals:
## Min 1Q Median 3Q Max
## -455126 -204924 -31449 136248 798682
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1124898 27355 41.122 <0.0000000000000002 ***
## Average_distance_fromCBD -13230 1354 -9.769 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 262600 on 342 degrees of freedom
## Multiple R-squared: 0.2182, Adjusted R-squared: 0.2159
## F-statistic: 95.43 on 1 and 342 DF, p-value: < 0.00000000000000022
#Test the main assumptions for linear regression
#Interpret and test the statistical significance of the regression intercept and slope.
lm(formula =Average_price_of_Suburb~Average_distance_fromCBD , data = dist_and_price )
##
## Call:
## lm(formula = Average_price_of_Suburb ~ Average_distance_fromCBD,
## data = dist_and_price)
##
## Coefficients:
## (Intercept) Average_distance_fromCBD
## 1124898 -13230
Hypotheses_model %>% confint()
## 2.5 % 97.5 %
## (Intercept) 1071092.61 1178702.85
## Average_distance_fromCBD -15893.37 -10565.84
- Regression equation to calculate price: \(Price in Dollar = \frac{1124898 - distance *13230}{}\)
Residuals: Min 1Q Median 3Q Max -20.232 -7.800 -0.708 5.666 32.636
Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.206e+01 1.593e+00 20.123 <2e-16 Average_price_of_Suburb -1.649e-05 1.688e-06 -9.769 <2e-16 — Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9.27 on 342 degrees of freedom Multiple R-squared: 0.2182, Adjusted R-squared: 0.2159 F-statistic: 95.43 on 1 and 342 DF, p-value: < 2.2e-16