RPubs link information

• http://rpubs.com/vikrant/asgn4

Introduction

• The report provides analysis of fuel consumption of new private cars.
• The aim of the report is to understand how fuel consumption by cars have improved over the years.

Introduction Cont.

• Engine capacity/volume affecs fuel consumption.
• The year in which car is manufactured affects how fuel efficient it is.
• The type of fuel used by the engine also affects it’s fuel consumtion.
• Engines which run on diesel tend to consume more fuel than those which run on petrol.

Problem Statement

Is there a difference in fuel consumption by cars made in year 2000 and 2011?

Data

• Data is collected from Average Fuel consumption.
• Data represents average fuel consumption of new private cars from year 2000 to 2011.
• Engine capacity and type of fuel consumed are also given.
• type is a nominal data, based on the type of fuel consumed. It can be either ‘Petrol’ or ‘Diesel’.

avgp <- read.csv("fuel_consumption.csv")

Data Cont.

• engineV is ordinal data with levels from ‘901 to 1000 cc’ to ‘> 3000 cc’.
• Apart from last level, each has a fixed interval of 99 cc.
• Fuel consumption for each year is represented under quantitave data.
• They are stored under the variable name of the year itself.

avgp$engineV <- factor(avgp$engineV, levels = avgp$engineV[1:22], ordered = TRUE)

Descriptive Statistics and Visualisation

• Visual summary of fuel consumption by cars in the year 2000

X2000.m <- mean(avgp$X2000)
X2000.sd <- sd(avgp$X2000)
ggplot(avgp, aes(X2000, fill = Type)) +
  geom_histogram(color = "black", binwidth = 1, position = "stack") +
  geom_vline(xintercept = c(X2000.m, X2000.m+X2000.sd, X2000.m-X2000.sd),
             colour = c("gold", rep("gray21", 2)), lwd = c(2, 1, 1)) +
  ggtitle("Distribution of fuel consumption of cars in the year 2000") +
  xlab("Fuel consumption in year 2000")

Descriptive statistics cont.

• Important sttistics for fuel consumption by cars in the year 2000.

avgdsummarize<- avgp %>% summarise(Min = min(X2000,na.rm = TRUE),
                                Q1 = quantile(X2000,probs = .25,na.rm = TRUE),
                                Median = median(X2000, na.rm = TRUE),
                                Q3 = quantile(X2000,probs = .75,na.rm = TRUE),
                                Max = max(X2000,na.rm = TRUE),
                                Mean = mean(X2000, na.rm = TRUE),
                                SD = sd(X2000, na.rm = TRUE),
                                Count = n())
knitr::kable(avgdsummarize)

Decsriptive Statistics Cont.

• Visual summary of fuel consumption by cars in the year 2011

X2011.m <- mean(avgp$X2011)
X2011.sd <- sd(avgp$X2011)
ggplot(avgp, aes(X2011, fill = Type)) +
  geom_histogram(color = "black", binwidth = 1, position = "stack") +
  geom_vline(xintercept = c(X2011.m, X2011.m+X2011.sd, X2011.m-X2011.sd),
             colour = c("gold", rep("gray21", 2)), lwd = c(2, 1, 1)) +
  ggtitle("Distribution of fuel consumption of cars in the year 2011") +
  xlab("Fuel consumption in year 2011")

Decsriptive Statistics Cont.

• Important sttistics for fuel consumption by cars in the year 2011.

avgpsummarize<-avgp %>% summarise(Min = min(X2011,na.rm = TRUE),
                       Q1 = quantile(X2011,probs = .25,na.rm = TRUE),
                       Median = median(X2011, na.rm = TRUE),
                       Q3 = quantile(X2011,probs = .75,na.rm = TRUE),
                       Max = max(X2011,na.rm = TRUE),
                       Mean = mean(X2011, na.rm = TRUE),
                       SD = sd(X2011, na.rm = TRUE),
                       Count = n()) 
knitr::kable(avgpsummarize)

Hypothesis Testing

• The null hypothesis is that there is no diference in average fuel consumption by cars between years 2000 and 2011.\[H_0: \mu_1 = \mu_2 \]

Hypothesis Testing Cont.

• The null hypothesis is that there is no diference in average fuel consumption by cars between years 2000 and 2011.\[H_0: \mu_1 = \mu_2 \]

• Alternate hypothesis being that there is a difference in average fuel comsumption by cars between years 2000 and 2011.\[H_A: \mu_1 \ne \mu_2\]

Hypothesis Testing Cont.

• First we have to verify our assumptions for the hypothesis testing
• From the QQplot below for fuel consumption in year 2000, we can see that all the datapoints are within the 95% confidence interval.

avgp$X2000 %>% qqPlot(dist="norm")

Hypothesis Testing Cont.

• From the QQplot below for fuel consumption in year 2011, we can see that all the datapoints are within the 95% confidence interval.

avgp$X2011 %>% qqPlot(dist="norm")

Hypothesis Testing Cont.

• With the normality established, we perform the two-sample t-test.

t.test(avgp$X2000 ,avgp$X2011,alternative = "two.sided")

## 
##  Welch Two Sample t-test
## 
## data:  avgp$X2000 and avgp$X2011
## t = 2.7085, df = 83.187, p-value = 0.008203
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.3104354 2.0263828
## sample estimates:
## mean of x mean of y 
##  7.834091  6.665682

• p-value = 0.008, which is less than significance level.
• The null hypothesis \(H_0\) can be rejected.

Discussion

• The test performed is statistically significant with p=0.008, df = 83.187, t = 2.708.
• Rejecting the null hypothesis, we can say that there is a difference in average fuel consumption by cars from year 2000 and year 2011.
• The average value of fuel consumption for year 2000 is 7.834.
• The average value of fuel consumption for year 2011 is 6.666.
• Over the years, fuel consumption of cars have improved.
• The investigation can further be strengthened by analysing how it has improved for diesel and petrol engines.

References

• Average Fuel Consumption, Anton Bobanev (May, 2017) https://www.kaggle.com/antfarol/average-fuel-consumption