Tutorial Week 2
2023-08-09
1.1
setwd("C:/Users/gabeg/Documents/Uni/Stat 5003/Week 2")
library(tidyverse)## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.5 v dplyr 1.0.7
## v tidyr 1.1.4 v stringr 1.4.0
## v readr 2.0.2 v forcats 0.5.1## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()## 1.1
melb <- read.csv('Melbourne_housing_FULL.csv')1.2
##1.2
melb_filter <- filter(melb, Suburb %in% c("Hawthorn", "Brunswick", "Craigieburn"))
## get Mean and Median Price
melb_filter %>%
group_by(Suburb) %>%
summarise(Num_properties = n(), Mean_price = mean(Price, na.rm = TRUE), Median_price = median(Price, na.rm = TRUE ), Mean_Building_Area = mean(BuildingArea, na.rm = TRUE), Median_Building_Area = median(BuildingArea, na.rm = TRUE))## # A tibble: 3 x 6
## Suburb Num_properties Mean_price Median_price Mean_Building_Area
## <chr> <int> <dbl> <dbl> <dbl>
## 1 Brunswick 444 977989. 950000 122.
## 2 Craigieburn 255 566173. 562500 161.
## 3 Hawthorn 428 1238074. 750500 144.
## # ... with 1 more variable: Median_Building_Area <dbl>Let’s Visualise the relationship between Price and Suburb
theme_set(
theme_bw()
)
ggplot(data = melb_filter,
aes(x = BuildingArea, y = Price/1000, color = Suburb)) +
geom_point() +
labs(title = "Property Price vs. Building Area by Suburb",
x = "Building Area in metres" ,
y = "Price in thousands")## Warning: Removed 709 rows containing missing values (geom_point).
## Let’s have a look at the spread of Building size per Suburb
boxplot( BuildingArea ~ as.factor(Suburb), melb_filter,
main = "Spread of Building Area Across Selected Suburbs",
ylab = "Building Area",
xlab = "Suburbs")
Lets have a look at the spread across our other variables
par( mfrow = c(2,2))
boxplot( Price/1000 ~ as.factor(Suburb), melb_filter,
main = "Price per Suburbs",
ylab = "Price in thousands",
xlab = "Suburbs")
boxplot( Landsize ~ as.factor(Suburb), melb_filter,
main = "Landsize per Suburbs",
ylab = "Landsize",
xlab = "Suburbs")
boxplot( Car ~ as.factor(Suburb), melb_filter,
main = "Carparks per Suburbs",
ylab = "Building Area",
xlab = "Suburbs")
boxplot( Rooms ~ as.factor(Suburb), melb_filter,
main = "Rooms per Suburbs",
ylab = "Rooms",
xlab = "Suburbs")
1.3
## 1.3
model <- lm(Price ~ BuildingArea, data = melb_filter)
coef(model)## (Intercept) BuildingArea
## 518192.115 3800.746summary(model)##
## Call:
## lm(formula = Price ~ BuildingArea, data = melb_filter)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3421769 -463874 -148030 259071 6052396
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 518192.1 66595.6 7.781 5.74e-14 ***
## BuildingArea 3800.7 408.2 9.311 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 730000 on 416 degrees of freedom
## (709 observations deleted due to missingness)
## Multiple R-squared: 0.1725, Adjusted R-squared: 0.1705
## F-statistic: 86.69 on 1 and 416 DF, p-value: < 2.2e-161.4a
##1.4
multi_model1 <- lm(Price/1000 ~ factor(Suburb) + BuildingArea, data = melb_filter)
coef(multi_model1)## (Intercept) factor(Suburb)Craigieburn factor(Suburb)Hawthorn
## 509.756694 -660.277321 400.715877
## BuildingArea
## 4.435441summary(multi_model1)##
## Call:
## lm(formula = Price/1000 ~ factor(Suburb) + BuildingArea, data = melb_filter)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4074.1 -248.5 -26.7 166.0 5479.9
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 509.7567 62.4510 8.163 3.99e-15 ***
## factor(Suburb)Craigieburn -660.2773 72.9115 -9.056 < 2e-16 ***
## factor(Suburb)Hawthorn 400.7159 72.5435 5.524 5.87e-08 ***
## BuildingArea 4.4354 0.3469 12.786 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 609.9 on 414 degrees of freedom
## (709 observations deleted due to missingness)
## Multiple R-squared: 0.425, Adjusted R-squared: 0.4208
## F-statistic: 102 on 3 and 414 DF, p-value: < 2.2e-16Interpreting the regression coeffiecients:
- All variables are statistically significant at 1% level.
- The base case in our dummy variable regression is the Suburb
Brunswick. The Hawthorn coefficient is positive which means, holding
Building Area constant the average price of property in Hawthorn is
$400715.90 (400.7159 * 1000) more than in Brunswick. The inverse is true
for Craigieburn as the coefficient is negative; holding Building Area
constant the average price of property in Craigieburn is 660277.3 less
than in Brunswick.
- This could be intuited by looking at the graph. If we compare the slopes of the 3 suburbs we see that Hawthorn is significantly steeper and Craigieburn is slightly flatter than Brunswick’s. This would also mean that an increase (decrease) in Building Area would lead to a larger increase (decrease) in Property Price.
- The intercept can be thought of as the lowest price to enter the property market. ie when a property has Building Area = 0 which is not practical but is a good proxy for a floor price for the Melbourne property market.
## Visualisation for 1.4a
ggplot(data = melb_filter,
aes(x = BuildingArea, y = Price/1000, color = Suburb)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE, fullrange = TRUE) +
labs(title = "Property Price vs. Building Area by Suburb",
x = "Building Area in metres" ,
y = "Price in thousands")## `geom_smooth()` using formula 'y ~ x'## Warning: Removed 709 rows containing non-finite values (stat_smooth).## Warning: Removed 709 rows containing missing values (geom_point).
1.4b
multi_model2 <- lm(Price/1000 ~ Suburb + BuildingArea + Car, data = melb_filter)
summary(multi_model2)##
## Call:
## lm(formula = Price/1000 ~ Suburb + BuildingArea + Car, data = melb_filter)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3417.3 -273.4 -59.2 252.5 5001.7
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 333.5607 67.0114 4.978 9.56e-07 ***
## SuburbCraigieburn -781.1077 73.7764 -10.588 < 2e-16 ***
## SuburbHawthorn 363.4368 71.1395 5.109 5.02e-07 ***
## BuildingArea 3.7617 0.3513 10.708 < 2e-16 ***
## Car 220.7405 34.6168 6.377 4.98e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 588.5 on 402 degrees of freedom
## (720 observations deleted due to missingness)
## Multiple R-squared: 0.477, Adjusted R-squared: 0.4718
## F-statistic: 91.66 on 4 and 402 DF, p-value: < 2.2e-16Interpreting the addition of Cars as an explanatory variable
Looking at the p-values from adding Car spaces to the linear regression model we see that Car is significant at the 1% level and the R-squared increases from 0.425 -> 0.477. This means that this model does a better job at explaining the variability of the actual data. However, a R-squared of 0.477 is not a very high score meaning our model does not do a great job at explaining the variability of property prices in general even if it is slightly better than before.
References
- Taboga, Marco (2021). “Dummy variable”, Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/fundamentals-of-statistics/dummy-variable.