RPubs link information

http://rpubs.com/vijetaashish/320626

Introduction

Total motor vehicle sales in Australia for the month of August 2017 alone was 100,809 which increased by 2.7% compared to last year. The sale of Vehicles, both passenger cars and sports utility, was robust in last few years.

Despite news in media that local automobile companies are struggling to cope competitive prices from import of cheaper car models and looking for government support to sustain, wondering what is giving momentum to total sales?

Introduction Cont.

• We studied the exchange rate AUD/USD movement to analyse if it correlates with the movement of monthly Total motor Vehicle sales.

• As we know that a depreciating Australian Dollar boosts exports and Australia exports cars especially four-wheel drive(4WD). In 2016, Australia exported AUD 2.7 million worth of road motor vehicles & parts (Data from Australia’s Department of Foreign Affairs and Trade)

Problem Statement

• Is total motor Vehicle sales in Australia driven by exchange rate (AUD/USD)? If Yes, how strong is the correlation?

• We will use Scatter plot to determine if there is any linear relation between variables.

• We perform Hypothesis Testing to determine if any correlation exists.

• Finally, determine the strength of correlation using Pearson’s Coefficient.

Data

• The data is sourced from authentic government website and is open data.

• Historical quantitative data is used.

• Vehicle Sales data type is ‘Ratio’ and exchange rate data is of type ‘Interval’.

• We study the data to find the ‘Explainable Variation’.

• The type of statistical data investigation carried out here is “Observational or Correlational Studies”.

Data Cont.

• AUD/USD is the exchange rate of AUD per one USD. The data is on monthly basis.

• Vehicles sales is whole number (units). Data is on monthly basis.

• Excel files are downloaded from website for data.

• Data is visualised in RStudio using R packages to understand the pattern and select appropriate statistical tool for ananlysis.

Descriptive Statistics and Visualisation

• We visualize the scatter plot bwteen 2 variables. Scatter plot suggests a positive and somewhat linear relation
• We used log transformation to try smoothen skewness to some extent.
• There is no missing data. They are few outliers but not very significant, so we ignore them.

#Check for any Linear relationship
plot(Vehicle_Sales ~ AUD_USD, data = Vehicle)

plot(log(Vehicle_Sales) ~ log(AUD_USD), data = Vehicle)

Data Visualisation continued…

par(mfrow=c(2,2))
Vehicle$AUD_USD %>%  hist(main = "AUD_USD")
log(Vehicle$AUD_USD) %>%  hist(main = "log(AUD_USD)")
Vehicle$Vehicle_Sales %>%  hist(main = "Vehicle_Sales")
log(Vehicle$Vehicle_Sales) %>%  hist(main = "log(Vehicle_Sales)")

Data Visualisation continued…

#Linear Model FIT

model <- lm(Vehicle_Sales ~ AUD_USD, data = Vehicle)
model %>% summary()

## 
## Call:
## lm(formula = Vehicle_Sales ~ AUD_USD, data = Vehicle)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -11920  -5350  -1457   2611  17201 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 52619.94    2875.59   18.30   <2e-16 ***
## AUD_USD       401.55      35.33   11.37   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7646 on 198 degrees of freedom
## Multiple R-squared:  0.3949, Adjusted R-squared:  0.3918 
## F-statistic: 129.2 on 1 and 198 DF,  p-value: < 2.2e-16

Data Visualisation continued…

plot(Vehicle_Sales ~ AUD_USD, data = Vehicle, xlab = "AUD_USD", ylab = "Total Vehicle Sales in Australia")
abline(model, col = "red")

Hypothesis Testing

• Is there any correlation between Vehicle Sales and exchange rate?
• Our Null Hypothesis is that there is no correlation (r). H0 : r = 0 (r is equal to zero) HA: r != 0 (r is not equal to zero)

#Hypothesis Testing
library(Hmisc)
bivariate<-as.matrix(dplyr::select(Vehicle, Vehicle_Sales,AUD_USD)) #Create a matrix of the variables to be correlated
rcorr(bivariate, type = "pearson")

##               Vehicle_Sales AUD_USD
## Vehicle_Sales          1.00    0.63
## AUD_USD                0.63    1.00
## 
## n= 200 
## 
## 
## P
##               Vehicle_Sales AUD_USD
## Vehicle_Sales                0     
## AUD_USD        0

# COnfidence Interval
library(psychometric)
r=cor(Vehicle$Vehicle_Sales, Vehicle$AUD_USD)
CIr(r = r, n = 200, level = .95)

## [1] 0.5364271 0.7056214

#Correlation
cor(Vehicle$Vehicle_Sales, Vehicle$AUD_USD)

## [1] 0.6283998

Discussion

• The relation between Vehicle_Sales and AUD/USD is not perfectly linear as explained by the value of R^2 = 0.39 (from linear regression model fit above). This means that only 39% of the variablility in Vehicle sales can be explained by a linear relationship with exchange rate.

• The correlation between Vehicle_Sales and AUD/USD is r = 0.63 and the p-value = 0, which we write as p < 0.001. Value of p is less than alpha of (0.05).

• Also, r = 0 is not captured by the 95% Confidence Interval [0.536, 0.706]

• So we reject our null hypothesis. This means, the result is statistically significant.

• Thus, there is a correlation between variables.However, the strength of correlation is not very strong.

• A depreciating AUD boosted export of the automobiles. Nearly one-third of Australia’s vehicle sales comes from its exports.

• Our analysis shows the exchange rate influences the vehicle sales to some extent. However, this is not the only factor. Other factors that can influence vehicle sales are disposable income, petrol prices, population growth, interest rate for vehicle loan etc.

References

http://dfat.gov.au

https://www.aph.gov.au/About_Parliament/Parliamentary_Departments/Parliamentary_Library/pubs/MSB

https://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=pet&s=rwtc&f=m