Housing_prices=read.csv("C:/Users/13996374/OneDrive - UTS/Documents/TEACHING/Autumn 2024/Technology research methods/R/Housing_prices.csv")

Number of variables and variable names

dim(Housing_prices)
## [1] 372   8
names(Housing_prices)
## [1] "ID"       "river"    "rooms"    "price"    "age"      "industry" "ptratio" 
## [8] "low_ses"
  1. Describe the characteristics of the study sample by the number of rooms/house (10%)
library(table1)
## 
## Attaching package: 'table1'
## The following objects are masked from 'package:base':
## 
##     units, units<-
table1(~ price + river + age + industry + ptratio + low_ses | rooms, data = Housing_prices)
4-room
(N=15)		 5-room
(N=27)		 6-room
(N=254)		 7-room
(N=76)		 Overall
(N=372)
price
Mean (SD) 17.3 (10.7) 14.0 (5.05) 18.9 (5.50) 28.8 (11.7) 20.5 (8.59)
Median [Min, Max] 13.8 [7.00, 50.0] 14.4 [5.00, 23.7] 19.4 [5.00, 50.0] 27.5 [7.50, 50.0] 19.8 [5.00, 50.0]
river
No 15 (100%) 23 (85.2%) 239 (94.1%) 67 (88.2%) 344 (92.5%)
Yes 0 (0%) 4 (14.8%) 15 (5.9%) 9 (11.8%) 28 (7.5%)
age
Mean (SD) 93.5 (15.9) 89.8 (20.4) 75.6 (24.3) 77.2 (21.1) 77.7 (23.6)
Median [Min, Max] 100 [37.8, 100] 96.2 [9.80, 100] 84.5 [6.00, 100] 82.7 [2.90, 100] 87.3 [2.90, 100]
industry
Mean (SD) 17.8 (2.23) 17.7 (5.43) 13.6 (6.16) 11.1 (6.53) 13.5 (6.32)
Median [Min, Max] 18.1 [9.90, 19.6] 18.1 [6.91, 27.7] 13.9 [2.18, 27.7] 9.90 [1.89, 19.6] 18.1 [1.89, 27.7]
ptratio
Mean (SD) 19.3 (1.94) 18.7 (2.31) 19.3 (1.71) 18.4 (1.81) 19.1 (1.82)
Median [Min, Max] 20.2 [14.7, 20.2] 20.1 [14.7, 21.2] 20.2 [14.7, 21.2] 18.0 [14.7, 21.0] 20.2 [14.7, 21.2]
low_ses
Mean (SD) 24.4 (11.4) 23.3 (6.75) 14.5 (5.37) 9.14 (6.25) 14.4 (7.15)
Median [Min, Max] 29.3 [3.26, 38.0] 24.0 [10.2, 34.4] 14.1 [5.08, 34.0] 6.79 [1.73, 25.8] 13.6 [1.73, 38.0]
  1. Develop and interpret a histogram for the distribution of house prices (10%)
library(ggplot2)
library(grid)
library(gridExtra) 
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following object is masked from 'package:gridExtra':
## 
##     combine
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(GGally)
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
library(ggthemes)
p = ggplot(data = Housing_prices, aes(x = price)) + geom_histogram(color = "black", fill = "blue") + labs(x = "Median housing prices (x USD 1,000)") + labs(y = "Count number")

p1 = ggplot(data = Housing_prices, aes(x = price, y = ..density..)) + geom_histogram(color = "black", fill = "blue") +  geom_density(col="red") + labs(x = "Median housing prices (x USD 1,000)") + labs(y = "Density")

grid.arrange(p, p1, nrow = 2, top = textGrob("Housing Prices Distribution", gp = gpar(fontsize = 15, font = 2)))
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(density)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

  1. Develop and interpret a box plot to describe the differences in housing prices among the number of rooms per household (10%)
p = ggplot(data = Housing_prices, aes(x = rooms, y = price, fill = rooms, col = rooms))

p1 = p + geom_boxplot(col = "black") + geom_jitter(alpha = 0.4) + labs(x = "Room numbers of each household", y = "Median housing prices (x USD 1,000)") + ggtitle("Box Plot of housing prices by room numbers of each household") + theme_bw()

p1

  1. Conduct a statistical test to determine whether housing prices were different among houses with different numbers of rooms. Interpret the findings (15%)

kruskal-Wallis Test

kruskal.test(price ~ rooms, data = Housing_prices)
## 
##  Kruskal-Wallis rank sum test
## 
## data:  price by rooms
## Kruskal-Wallis chi-squared = 75.504, df = 3, p-value = 2.826e-16

ANOVA Test

anova_test= aov(price ~ rooms, data = Housing_prices)
summary(anova_test)
##              Df Sum Sq Mean Sq F value Pr(>F)    
## rooms         3   7162  2387.2   43.49 <2e-16 ***
## Residuals   368  20202    54.9                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
  1. Determine which particular number of rooms/house had different house prices using the Tukey posthoc test. Fill in the following table and interpret the findings (20%)
tukey_result = TukeyHSD(anova_test)
tukey_result
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = price ~ rooms, data = Housing_prices)
## 
## $rooms
##                    diff       lwr       upr     p adj
## 5-room-4-room -3.215556 -9.373321  2.942210 0.5331459
## 6-room-4-room  1.603780 -3.477109  6.684668 0.8475492
## 7-room-4-room 11.511053  6.108559 16.913546 0.0000004
## 6-room-5-room  4.819335  0.948716  8.689954 0.0077590
## 7-room-5-room 14.726608 10.442544 19.010672 0.0000000
## 7-room-6-room  9.907273  7.407162 12.407384 0.0000000
tukey_results <- data.frame(
  
  Comparisons = c("5-room houses vs. 4-room houses","6-room houses vs. 4-room houses", "7-room houses vs. 4-room houses", "6-room houses vs. 5-room houses", "7-room houses vs. 5-room houses", "7-room houses vs. 6-room houses"),
  
  Mean_Differences_in_housing_price= c("-3.21 (-9.37, 2.94)","1.60 [-3.48, 6.68]","11.51 [6.11, 16.91]","4.82 [0.95, 8.69]","14.73 [10.44, 19.01]","9.91 [7.41, 12.41]"),
  
  P_Value = c("0.5331", "0.8475", "0.0000", "0.0078", "0.0000", "0.0000")
)
print(tukey_results, row.names = FALSE)
##                      Comparisons Mean_Differences_in_housing_price P_Value
##  5-room houses vs. 4-room houses               -3.21 (-9.37, 2.94)  0.5331
##  6-room houses vs. 4-room houses                1.60 [-3.48, 6.68]  0.8475
##  7-room houses vs. 4-room houses               11.51 [6.11, 16.91]  0.0000
##  6-room houses vs. 5-room houses                 4.82 [0.95, 8.69]  0.0078
##  7-room houses vs. 5-room houses              14.73 [10.44, 19.01]  0.0000
##  7-room houses vs. 6-room houses                9.91 [7.41, 12.41]  0.0000