HW-1- Anej Levpuscek MVA
Anej Levpuscek
2024-01-07
Dataset was used from Kaggle: https://www.kaggle.com/datasets/pushpakhinglaspure/used-car-price-prediction
Research Question
Does average selling price of the car differ between manual and automatic cars?
#install.packages("readxl")
library(readxl)## Warning: package 'readxl' was built under R version 4.3.2mydata <- read_xlsx("~/IMB/Mutivariat analysis/car data.xlsx")
head(mydata)## # A tibble: 6 × 9
## Car_Name Year Selling_Price Present_Price Kms_Driven Fuel_Type Seller_Type
## <chr> <dbl> <dbl> <dbl> <dbl> <chr> <chr>
## 1 ritz 2014 335 559 27000 Petrol Dealer
## 2 sx4 2013 475 954 43000 Diesel Dealer
## 3 ciaz 2017 725 985 6900 Petrol Dealer
## 4 wagon r 2011 285 415 5200 Petrol Dealer
## 5 swift 2014 46 687 42450 Diesel Dealer
## 6 vitara bre… 2018 925 983 2071 Diesel Dealer
## # ℹ 2 more variables: Transmission <chr>, Owner <dbl>Explanation of dataset
- Unit of observation: cars
- Sample size: n = 301
- Definition of variables:
- Year - the car’s manufacturing year
- Selling_Price - The actual price at which the car was sold
- Present_Price: The currrent price at which the car is listed
- Kms_Driven: total distance driven in kilometers
- Fuel_Type: Categorical variable, specifying the car’s fuel type (e.g., petrol, diesel, hybrid, electric)
- Seller_Type: Categorical variable, indicting whether the seller is the individual or a dealer
- Transmission: Categorical variable, specifying the car’s transmission type (e.g., manual, automatic)
- Owner: Categorical variable, indicating whether the car has had previous owners or is being sold by the first owner
I have a sample on 301 units, therefore I will make random sample of 100 units, for the purpose of testing hypothesis and normality
set.seed(1) #Setting initial point of sampling
mydata <- mydata[sample(nrow(mydata),100),]Data manipulations
#for the purpose of the easier analysis, I will exclude some of the variables I won't use in the analysis
mydata2 <- mydata[,c(-2,-6,-7,-9)]
head(mydata2)## # A tibble: 6 × 5
## Car_Name Selling_Price Present_Price Kms_Driven Transmission
## <chr> <dbl> <dbl> <dbl> <chr>
## 1 Hero Passion Pro 45 55 1000 Manual
## 2 Honda CB Hornet 160R 8 87 3000 Manual
## 3 city 335 11 87934 Manual
## 4 city 67 10 18828 Manual
## 5 TVS Wego 25 52 22000 Automatic
## 6 innova 349 1346 197176 Manual#creating new variable and informing R that we have non-numerical variable
mydata2$TransmissionF <- factor(mydata2$Transmission,
levels = c("Manual", "Automatic"),
labels =c("Manual", "Automatic"))
head(mydata2)## # A tibble: 6 × 6
## Car_Name Selling_Price Present_Price Kms_Driven Transmission TransmissionF
## <chr> <dbl> <dbl> <dbl> <chr> <fct>
## 1 Hero Passio… 45 55 1000 Manual Manual
## 2 Honda CB Ho… 8 87 3000 Manual Manual
## 3 city 335 11 87934 Manual Manual
## 4 city 67 10 18828 Manual Manual
## 5 TVS Wego 25 52 22000 Automatic Automatic
## 6 innova 349 1346 197176 Manual Manualsummary(mydata2[,c(-1,-5)])## Selling_Price Present_Price Kms_Driven TransmissionF
## Min. : 2.0 Min. : 10.0 Min. : 1000 Manual :86
## 1st Qu.: 25.0 1st Qu.: 76.0 1st Qu.: 14875 Automatic:14
## Median : 63.0 Median : 136.0 Median : 33494
## Mean : 216.7 Mean : 478.5 Mean : 35699
## 3rd Qu.: 272.5 3rd Qu.: 655.8 3rd Qu.: 48825
## Max. :1999.0 Max. :3596.0 Max. :197176library(psych)
describe(mydata2[,c(-1,-5,-6)])## vars n mean sd median trimmed mad min max
## Selling_Price 1 100 216.67 338.30 63 140.72 84.51 2 1999
## Present_Price 2 100 478.51 717.40 136 308.20 153.45 10 3596
## Kms_Driven 3 100 35698.61 29287.81 33494 32288.20 25788.34 1000 197176
## range skew kurtosis se
## Selling_Price 1997 2.61 8.15 33.83
## Present_Price 3586 2.65 7.41 71.74
## Kms_Driven 196176 2.15 8.47 2928.78Explanations of parameters
- Selling_Price - min: The lowest selling price (The actual price at which the car was sold) of the car in the sample was 2 units.
- Present_price - mean: The present price of the car (The currrent price at which the car is listed) was on average 478.51 units.
- Kms_Driven - median: Half of the cars in in the sample had less or equal to 33494 kilometers driven and half of the cars had more than 33494 kilometers driven.
- Selling_Price - skewness: Skewness value of 2.61 for variable Selling_Price indicates that the distribution of selling price is right-skewed or positively skewed.
Research Question
Does average selling price of the car significantly differ between Manual and Automatic cars?
Statistical hypothesis
- H0: There is no significant difference in average selling price between manual and automatic cars
- H1: There is a significant difference in average selling price between manual and automatic cars
Assumptions:
- Variable is numeric (Selling_Price is numeric variable)
- The distribution of the variable is normal in both populations (This will be tested with Shapiro Wilk’s test)
- The data must come from two independent populations (Manual and automatic cars are independent)
- Variable has the same variance in both populations (this assumtion is often violated, we will apply Welch correction)
library(ggplot2)##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alphaggplot(mydata2, aes(x = Selling_Price)) +
geom_histogram(binwidth = 30, colour="gray") +
facet_wrap(~TransmissionF, ncol = 1) +
ylab("Frequency")
Shapiro-Wilk Test for Normality
- H0: Variable Selling_Price is normally distributed in both groups
- H1: Variable Selling_price is not normally distributed in both groups
library(rstatix)## Warning: package 'rstatix' was built under R version 4.3.2##
## Attaching package: 'rstatix'## The following object is masked from 'package:stats':
##
## filterlibrary(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionmydata2 %>%
group_by(TransmissionF) %>%
shapiro_test(Selling_Price)## # A tibble: 2 × 4
## TransmissionF variable statistic p
## <fct> <chr> <dbl> <dbl>
## 1 Manual Selling_Price 0.704 6.97e-12
## 2 Automatic Selling_Price 0.528 9.94e- 6- We reject the normality assumption for both groups. The corresponding p values are both p<0.001
library(psych)
describeBy(mydata2$Selling_Price, mydata2$TransmissionF)##
## Descriptive statistics by group
## group: Manual
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 86 208.06 300.49 65 144.4 88.96 2 1425 1423 1.99 3.63 32.4
## ------------------------------------------------------------
## group: Automatic
## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 14 269.57 526.94 51 146.67 40.03 15 1999 1984 2.48 5.32
## se
## X1 140.83Alternative non-parametrical test; Wilcoxon Rank Sum Test
- H0: Distribution location of Selling Price is the same for automated and manual cars
- H1: Distributionlocation of Selling price is not the same for automated and manual cars
wilcox.test(mydata2$Selling_Price ~ mydata2$TransmissionF,
paired = FALSE,
correct = FALSE,
exact = FALSE,
alternative = "two.sided")##
## Wilcoxon rank sum test
##
## data: mydata2$Selling_Price by mydata2$TransmissionF
## W = 574.5, p-value = 0.7847
## alternative hypothesis: true location shift is not equal to 0- We can not reject the null hypothesis (p=0.79).
library(effectsize)##
## Attaching package: 'effectsize'## The following objects are masked from 'package:rstatix':
##
## cohens_d, eta_squared## The following object is masked from 'package:psych':
##
## phieffectsize(wilcox.test(mydata2$Selling_Price ~ mydata2$TransmissionF,
paired = FALSE,
correct = FALSE,
exact = FALSE,
alternative = "two.sided"))## r (rank biserial) | 95% CI
## ---------------------------------
## -0.05 | [-0.36, 0.27]interpret_rank_biserial(-0.05)## [1] "very small"
## (Rules: funder2019)Conclusion
Based on the sample data, we don’t have enough evidence that there is a significant difference in selling price between manual and automatic cars (p=0.79), the effect size is very small, |r|=0.05.
As assumptions are not met, it’s better to use non-parametric test, however, we can still show the results of the parametric test:
Independent Samples
t.test(mydata2$Selling_Price ~ mydata2$TransmissionF,
paired = FALSE,
var.equal = FALSE,
alternative = "two.sided")##
## Welch Two Sample t-test
##
## data: mydata2$Selling_Price by mydata2$TransmissionF
## t = -0.42566, df = 14.407, p-value = 0.6766
## alternative hypothesis: true difference in means between group Manual and group Automatic is not equal to 0
## 95 percent confidence interval:
## -370.6404 247.6139
## sample estimates:
## mean in group Manual mean in group Automatic
## 208.0581 269.5714- H0: There is no significant difference in average selling price between manual and automatic cars
- H1: There is a significant difference in average selling price between manual and automatic cars
library(effectsize)
effectsize::cohens_d(mydata2$Selling_Price ~ mydata2$TransmissionF,
pooled_sd = FALSE)## Cohen's d | 95% CI
## -------------------------
## -0.14 | [-0.80, 0.52]
##
## - Estimated using un-pooled SD.interpret_cohens_d(0.14, rules = "sawilowsky2009")## [1] "very small"
## (Rules: sawilowsky2009)Conclusion
- Based on the sample data we can not reject the null hypothesis (p=0.68), we can not say that that the average selling price differ between manual and automatic cars. (the effect size is very small, d=0,14). Once again for our data set its better to non-parametric test (as normality is not met), this is just to show the results of parametric test as well.