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Introduction

• The following link will help you with creating R Markdown Slidy Presentations
• http://rmarkdown.rstudio.com/slidy_presentation_format.html
• Don’t forget about Bootcamp 4
• A good introduction provides a brief background to the problem, defines important terms, and leads to a strong rationale.

Introduction Cont.

• The automotive industry comprises of a huge variety of activities and contributes majorly to the global economy.
• However, the industry faces certain hurdles in today’s technologically advanced world such as mileage, miles per gallon (mpg), various types engine size for different models of it’s company and taxes amongst many other factor.
• To overcome these hurdles, we tried to compare the models from year 1996 to 2060(the future models under process) on the basis of mpg and mileage along with the size of the engine.
• The variables we are considering for this analysis are mpg(miles per gallon), mileage of a car and engine size.
• The main objective is to conduct a Hypothesis test and draw conclusions from the findings. For the hypothesis, we have considered the mpg of the models of Ford cars. By conducting the hypothesis test, we will draw statistical inference on the following variables: a) mileage, b) mpg, c) engine size. This will provide informative knowledge on Ford cars as a whole.

Problem Statement

• The automotive industry is well known for its contribution toward harming the environment (like pollution, global warming, etc). Some of the factors responsible for these issues are as follows: a. Engine parts, b. Fuel type, c. Size of engine and d. miles per gallon
• Miles per Gallon (mpg) is an important metric in defining whether or not a car is cost effective, in other words, its affordability.
• It is recommended that cars have an average of 50 mpg in order to operate smoothly and reduce the CO2 emissions.
• The data-set used for our analysis revolves around myriad models of Ford cars from year 1996 to 2020. One sample t-test has been performed to check whether the recommended mpg is being put to practice or not.

Data

ford = read.csv("ford.csv")
str(ford)

## 'data.frame':    17966 obs. of  9 variables:
##  $ model       : chr  " Fiesta" " Focus" " Focus" " Fiesta" ...
##  $ year        : int  2017 2018 2017 2019 2019 2015 2019 2017 2019 2018 ...
##  $ price       : int  12000 14000 13000 17500 16500 10500 22500 9000 25500 10000 ...
##  $ transmission: chr  "Automatic" "Manual" "Manual" "Manual" ...
##  $ mileage     : int  15944 9083 12456 10460 1482 35432 2029 13054 6894 48141 ...
##  $ fuelType    : chr  "Petrol" "Petrol" "Petrol" "Petrol" ...
##  $ tax         : int  150 150 150 145 145 145 145 145 145 145 ...
##  $ mpg         : num  57.7 57.7 57.7 40.3 48.7 47.9 50.4 54.3 42.2 61.4 ...
##  $ engineSize  : num  1 1 1 1.5 1 1.6 1 1.2 2 1 ...

ford$model = factor(ford$model)
ford$year = factor(ford$year, levels = levels(as.factor(ford$year)), ordered = TRUE)
ford$price = factor(ford$price, levels = levels(as.factor(ford$price)), ordered = TRUE)

• The data source has been taken from Kaggle.
• https://www.kaggle.com/datasets/adhurimquku/ford-car-price-prediction

Data Cont.

• The data-set comprises of 17966 observations and 9 variables such as year, mpg, mileage, model, etc.
• The necessary variables for conducting our analysis are described as follows:

1. mpg- Miles per gallon is a numeric variable that provides us information on how far a car can travel for every gallon of fuel it consumes.

2. mileage- It is an efficiency metric that assists in measuring the car’s financial and economic affordability.

3. engineSize- The engine size determines the amount of power the engine can produce which affects the fuel consumption of a car.

Descriptive Statistics and Visualisation

• In order to achieve the main objective of our analysis, it is essential that we visualise the data. By doing so, we will gain insights to question such as:
  1. The average mpg used by the listed models of the Ford cars.
  2. The most frequent distance covered by a car (in miles).
  3. Comparison analysis of mpg vs mileage to the best point of reference between cost effective and performance.
• Initial insights to the above questions can be answered by conducting descriptive statistics on the following variables: a. mpg, b. mileage, c. engineSize.
• The below summary statistics describes the range, mean, median, quantile 1 and 3, standard deviation and missing values.
• Below are the R chunks implemented for the above mentioned functions.

ford <- ford[ford$tax != 0,]

mileage_summary <- ford %>% summarise(Parameter = "mileage",
                               Min = min(mileage,na.rm = TRUE),
                               Q1 = quantile(mileage,probs = .25,na.rm = TRUE),
                               Median = median(mileage, na.rm = TRUE),
                               Q3 = quantile(mileage,probs = .75,na.rm = TRUE), 
                               Max = max(mileage,na.rm = TRUE),
                               Mean = mean(mileage, na.rm = TRUE),
                               SD = sd(mileage, na.rm = TRUE), 
                               n = n(),Missing = sum(is.na(mileage)))

mpg_summary <- ford %>% summarise(Parameter = "mpg",
                               Min = min(mpg,na.rm = TRUE),
                               Q1 = quantile(mpg,probs = .25,na.rm = TRUE),
                               Median = median(mpg, na.rm = TRUE),
                               Q3 = quantile(mpg,probs = .75,na.rm = TRUE), 
                               Max = max(mpg,na.rm = TRUE),
                               Mean = mean(mpg, na.rm = TRUE),
                               SD = sd(mpg, na.rm = TRUE), 
                               n = n(),Missing = sum(is.na(mpg)))

engineSize_summary <- ford %>% summarise(Parameter = "engineSize",
                               Min = min(engineSize,na.rm = TRUE),
                               Q1 = quantile(engineSize,probs = .25,na.rm = TRUE),
                               Median = median(engineSize, na.rm = TRUE),
                               Q3 = quantile(engineSize,probs = .75,na.rm = TRUE), 
                               Max = max(engineSize,na.rm = TRUE),
                               Mean = mean(engineSize, na.rm = TRUE),
                               SD = sd(engineSize, na.rm = TRUE), 
                               n = n(),Missing = sum(is.na(engineSize)))

table1<-ford %>% group_by(fuelType) %>% summarise(Parameter = "mpg",
                               Min = min(mpg,na.rm = TRUE),
                               Q1 = quantile(mpg, probs = .25,na.rm = TRUE),
                               Median = median(mpg, na.rm = TRUE),
                               Q3 = quantile(mpg,probs = .75,na.rm = TRUE),
                               Max = max(mpg,na.rm = TRUE),
                               Mean = mean(mpg, na.rm = TRUE),
                               SD = sd(mpg, na.rm = TRUE),
                               range = max(mpg,na.rm = TRUE) - min(mpg,na.rm = TRUE),
                               n = n(),Missing = sum(is.na(mpg)))
knitr::kable(table1)

Decsriptive Statistics Cont.

The combined summary statistics of the Ford data-set has been described as follows:

1. mileage_summary

• The maximum number of mileage of a model of Ford Car in general is seen to be 177644 across the years from 1996 to 2020 whereas the lowest number of trips has reached 1 across the decades. A mean of 22107.46 and median of 16816 are considered to have achieved by the company across the years.

2. mpg_summary (Miles per Gallon)

• The range of mpg spreads anywhere between 20.8 and 201.8 in the given time frame. The average distance covered by a Ford car’s model, however, is 57.5.

3. engineSize_summary

• The engine size ranged between 1 to 5. The average size for the Ford models is around 1.4.

table2 <- rbind(mileage_summary, mpg_summary, engineSize_summary)
knitr::kable(table2)

Decsriptive Statistics Cont.

• The above mentioned variables, mpg and mileage, were used to plot the histogram and scatter plot. We concluded some intriguing results based on the visualisations given below:

1. Miles per Gallon

• There is a steep rise in the number of mpg of the various models of Ford cars, however the frequency of the number of mpg declines even more sharply. Therefore, we can infer that majority of the Ford car models meet the industry standards of 50 mpg.

2. Number of Miles traveled

• The highest frequency of miles covered by the various models of Ford cars occurs at 20,000 mileage range, however the occurrences of the various Ford car models decrease steadily as the mileage increases from 40,000 onwards.

3. Number of mileages covered based on mpg

• The scatter-plot maintains a steady trend as the mileage increases as the number of mpg stays within the same range.

• However, majority of the car models have their mpg below 100 making it consistent even if the mileage increases for it.

• Below are the R chunks implemented for the above mentioned functions.

# histogram
ford$mpg %>%  hist(col="grey", ylim=c(0,7000), xlim=c(0,300), xlab="Number of mpg",main="Histogram of Number of Miles per Gallon")

ford$mileage %>%  hist(col="grey",ylim=c(0,5000), xlim=c(0,200000), xlab="Mileage",main="Histogram of Number of Miles Travelled")

#Scatter plot
ford %>% plot(mpg ~ mileage, data = .,ylab="Miles per gallon", xlab="Mileage",col="blue",main="Mileage covered for every MPG  ")

# Decsriptive Statistics Cont.

Boxplot of Miles per Gallon(mpg) showcasing outliers:

• Analysing the boxplot below, we can see that there is one extreme outlier in comparison to the other few outliers that are placed just below 100% that there are a few outliers below 100%.

• In contrast, there are a majority of outliers below the 40% mark. there are some models that have very low mpg wherein most of the outliers with lower percentage ranged below 40%. There are a few assumptions that can be made for this. One such possible assumption might be that a particular model of Ford car gives very low mileage, ranking those particular car models at a lower purchase or use preference. This makes them a less preferred choice for people wishing to buy a car for long distance travels.

• Below are the R chunks implemented for the above mentioned functions.

# boxplot
plot1 <- boxplot(ford$mpg, main="Boxplot of Rate of Mileage with outliers", ylab= "Percentage of miles traveled")

Hypothesis Testing

• The Null Hypothesis (H0) states that the recommended average Miles per Gallon equal to the value of 50 is being followed by Ford Cars.
• The Alternate Hypothesis (HA) states that the recommended average Miles per Gallon equal to the value of 50 is not being followed by Ford Cars.
• For the purpose of our analysis, we have utilized the significance level (alpha) for testing at 5%.
• The mathematical equation for the Hypothesis testing as follows:

model1 <- t.test(ford$mpg, mu = 50)

model1

## 
##  One Sample t-test
## 
## data:  ford$mpg
## t = 83.688, df = 15812, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  56.16983 56.46577
## sample estimates:
## mean of x 
##   56.3178

\[H_0: \mu_1 = 50 \]

\[H_A: \mu_1 \ne 50 \]

Hypothesis cont.

• Upon conducting the hypothesis test, the following results have been obtained:

1. t-value = 104.67
2. p-value < 2.2e-16
3. Confidence interval for 95% : 57.75891, 58.05505

• Since the p-value is less than 0.05, we reject the null hypothesis. This implies that the recommended average miles per gallon (value of 50) is not being followed by Ford cars.

Discussion

• From the results obtained it is evident that the average mileage of a Ford car from 1996 to 2020 is around 22110.
• Subsequently, the engine size of most of the models is about 1.5 units. This might helps us to determine the average fuel consumption and motivate us to look for some ways to reduce that figure.
• Addition of the country variable in this data-set would have helped us in obtained some customized results. This limitation bounds us to make any specific assumptions or hypothesis for our calculations.
• These findings may also takes us towards the direction of climatic conditions, fuel consumption rate, manufacturing of engine, etc. Further discussing these pointers may guide us to find answers to the following questions:
  1. Which fuel type gave better mileage?
  2. which model is commonly used by the people and what is it’s average mpg for a particular year.
  3. Tax and the mileage of a particular car model for two different price ranges.

References

• Australian Industry and Skills Committee 2018, Automotive, National Industry Insights Report.(Australian Industry and Skills Committee 2018)

• Ford Car Price Prediction n.d., www.kaggle.com, https://www.kaggle.com/datasets/adhurimquku/ford-car-price-prediction

• www.hiltongarage.co.uk. (n.d.). What makes a good MPG? - Hilton Garage Limited. [online] Available at: https://www.hiltongarage.co.uk/blog/what-makes-a-good-mpg

• carwow.co.uk. (n.d.). What is mpg? How is it calculated? [online] Available at: https://www.carwow.co.uk/guides/running/what-is-mpg-0255#gref

• stasha (n.d.). Good mileage for a used car | Policy Advice. [online] policyadvice.net. Available at: https://policyadvice.net/insurance/guides/good-mileage-for-used-car/ [Accessed 29 May 2022].

• Car Keys. (n.d.). What does engine size mean? [online] Available at: https://www.carkeys.co.uk/guides/what-does-engine-size-mean [Accessed 29 May 2022].