AirlinePricing
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airline_df<-read.csv("./AirlinePricingData.csv")
air_df <- airline_df [,c("Price","AdvancedBookingDays","FlyingMinutes","Capacity","SeatPitch","SeatWidth")]
library(psych)
describe(air_df)## vars n mean sd median trimmed mad min
## Price 1 305 5394.54 2388.29 4681 4984.80 1052.65 2607
## AdvancedBookingDays 2 305 28.90 22.30 30 28.50 34.10 2
## FlyingMinutes 3 305 136.03 4.71 135 135.80 7.41 125
## Capacity 4 305 176.36 32.39 180 172.19 14.83 138
## SeatPitch 5 305 30.26 0.93 30 30.17 0.00 29
## SeatWidth 6 305 17.41 0.49 17 17.38 0.00 17
## max range skew kurtosis se
## Price 18015 15408 2.26 6.41 136.75
## AdvancedBookingDays 61 59 0.03 -1.68 1.28
## FlyingMinutes 145 20 0.28 -0.33 0.27
## Capacity 303 165 2.11 5.91 1.85
## SeatPitch 33 4 1.03 0.61 0.05
## SeatWidth 18 1 0.37 -1.86 0.03Q.1.a Correlation matrix for the variables {“Price”, “AdvancedBookingDays”, “FlyingMinutes”, “Capacity”, “SeatPitch”, “SeatWidth”}
Types of Correlations
Pearson, Spearman and Kendall
- The Pearson product moment correlation assesses the degree of linear relationship between two quantitative variables.
- Spearman’s rank-order correlation coefficient assesses the degree of relationship between two rank-ordered variables.
- Kendall’s tau is nonparametric measure of rank correlation.
Correlation (Pearsons) among selected columns
# Pearson product-moment correlation coefficients stored in 'matrix'
matrix <- cor(air_df)
# round upto 2 decimal places
round(matrix, 2) ## Price AdvancedBookingDays FlyingMinutes Capacity
## Price 1.00 -0.01 -0.02 -0.03
## AdvancedBookingDays -0.01 1.00 0.01 -0.01
## FlyingMinutes -0.02 0.01 1.00 -0.32
## Capacity -0.03 -0.01 -0.32 1.00
## SeatPitch 0.07 -0.01 -0.03 0.51
## SeatWidth -0.06 0.05 -0.18 0.45
## SeatPitch SeatWidth
## Price 0.07 -0.06
## AdvancedBookingDays -0.01 0.05
## FlyingMinutes -0.03 -0.18
## Capacity 0.51 0.45
## SeatPitch 1.00 0.32
## SeatWidth 0.32 1.00Correlation (Spearman) among selected columns
# Pearson product-moment correlation coefficients stored in 'matrix2'
matrix2 <- cor(air_df,method="spearman")
# round upto 2 decimal places
round(matrix2, 2) ## Price AdvancedBookingDays FlyingMinutes Capacity
## Price 1.00 -0.09 0.02 -0.07
## AdvancedBookingDays -0.09 1.00 0.02 -0.01
## FlyingMinutes 0.02 0.02 1.00 -0.34
## Capacity -0.07 -0.01 -0.34 1.00
## SeatPitch 0.15 0.00 0.02 0.22
## SeatWidth -0.15 0.10 -0.18 0.54
## SeatPitch SeatWidth
## Price 0.15 -0.15
## AdvancedBookingDays 0.00 0.10
## FlyingMinutes 0.02 -0.18
## Capacity 0.22 0.54
## SeatPitch 1.00 0.32
## SeatWidth 0.32 1.00Q.1.b Correlations (Pearson) with significance levels
The rcorr() function in the Hmisc package produces correlations/covariances and significance levels for pearson and spearman correlations.
library(Hmisc)
air_mat <- rcorr(as.matrix(air_df), type="pearson")
air_matQ.1.b Correlations (Spearman) with significance levels
The rcorr() function in the Hmisc package produces correlations/covariances and significance levels for pearson and spearman correlations.
library(Hmisc)
air_mat2 <- rcorr(as.matrix(air_df), type="spearman")
air_mat2Q.1.c R code to visualize the correlation matrix 
Q.1.e Corrgram
====================================================
## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric##
## Attaching package: 'PerformanceAnalytics'## The following object is masked from 'package:graphics':
##
## legend
Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.
#2a
z<-read.csv("./AirlinePricingData.csv")
abc<-read.csv("./AirlinePricingData.csv")
t.test(z$Price,mu=5000,alternative = "greater")##
## One Sample t-test
##
## data: z$Price
## t = 2.8851, df = 304, p-value = 0.002096
## alternative hypothesis: true mean is greater than 5000
## 95 percent confidence interval:
## 5168.918 Inf
## sample estimates:
## mean of x
## 5394.544#2b
am=subset(abc,abc$Departure=="AM")
pm=subset(abc,abc$Departure=="PM")
t.test(am$Price,pm$Price,alternative = "greater")##
## Welch Two Sample t-test
##
## data: am$Price and pm$Price
## t = 1.736, df = 296.58, p-value = 0.0418
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## 22.71262 Inf
## sample estimates:
## mean of x mean of y
## 5598.893 5140.610#2c
diw=subset(abc,abc$IsDiwali==1)
nondiw=subset(abc,abc$IsDiwali==0)
t.test(diw$Price,nondiw$Price,alternative = "greater")##
## Welch Two Sample t-test
##
## data: diw$Price and nondiw$Price
## t = 2.9799, df = 244.52, p-value = 0.001587
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## 371.7482 Inf
## sample estimates:
## mean of x mean of y
## 5897.479 5063.810#2d
ai=subset(abc,abc$Airline=="Air India")
ind=subset(abc,abc$Airline=="IndiGo")
t.test(ai$Price,ind$Price,alternative = "greater")##
## Welch Two Sample t-test
##
## data: ai$Price and ind$Price
## t = 2.7205, df = 87.71, p-value = 0.00393
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## 566.0833 Inf
## sample estimates:
## mean of x mean of y
## 6335.000 4879.525#Question 3
modl=lm(z$Price~z$AdvancedBookingDays)
summary(modl)##
## Call:
## lm(formula = z$Price ~ z$AdvancedBookingDays)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2786.5 -1320.8 -688.9 351.2 12594.0
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5422.959 224.497 24.16 <2e-16 ***
## z$AdvancedBookingDays -0.983 6.154 -0.16 0.873
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2392 on 303 degrees of freedom
## Multiple R-squared: 8.422e-05, Adjusted R-squared: -0.003216
## F-statistic: 0.02552 on 1 and 303 DF, p-value: 0.8732