Effect of Advance Booking on Airline Ticket Pricing in India
Sameer Mathur
Regression Analysis
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PART 1: READING AND DESCRIBING DATA
Number of Rows and Columns
[1] 8187 23
Name of the Data Variables
[1] "FlightNumber" "Airline" "DepartureCity"
[4] "ArrivalCity" "DepartureTime" "ArrivalTime"
[7] "Departure" "Fly" "FlyingTime"
[10] "Aircraft" "PlaneModel" "Capacity"
[13] "SeatPitch" "SeatWidth" "DataCollectionDate"
[16] "DateDeparture" "DayDeparture" "Weekend"
[19] "Price" "AdvBookDays" "Diwali"
[22] "DayBeforeDiwali" "DayAfterDiwali"
Descriptive Statistics
vars n mean sd median min max
FlightNumber* 1 8187 874.45 513.40 866 1.0 1765
Airline* 2 8187 2.27 0.90 2 1.0 4
DepartureCity* 3 8187 36.11 20.09 42 1.0 79
ArrivalCity* 4 8187 37.25 18.73 41 1.0 76
DepartureTime 5 8187 1129.12 589.76 1020 5.0 2345
ArrivalTime 6 8187 1194.21 610.53 1115 0.0 2359
Departure* 7 8187 1.41 0.49 1 1.0 2
Fly* 8 8187 2.66 0.98 3 1.0 4
FlyingTime 9 8187 112.46 35.80 110 40.0 195
Aircraft* 10 8187 2.30 0.62 2 1.0 4
PlaneModel* 11 8187 55.47 26.22 61 1.0 122
Capacity 12 8187 165.44 36.79 180 50.0 423
SeatPitch 13 8187 30.22 1.23 30 29.0 40
SeatWidth 14 8187 17.61 0.59 18 16.2 21
DataCollectionDate* 15 8187 3.76 0.98 4 1.0 7
DateDeparture* 16 8187 13.16 9.06 12 1.0 29
DayDeparture* 17 8187 4.75 1.65 5 1.0 7
Weekend* 18 8187 1.17 0.38 1 1.0 2
Price 19 8187 5555.89 3219.96 4778 637.0 43454
AdvBookDays 20 8187 14.65 9.78 16 1.0 39
Diwali* 21 8187 1.40 0.49 1 1.0 2
DayBeforeDiwali* 22 8187 1.20 0.40 1 1.0 2
DayAfterDiwali* 23 8187 1.20 0.40 1 1.0 2
Correlation Matrix
Price AdvBookDays FlyingTime SeatPitch SeatWidth Capacity
Price 1.00 -0.24 0.31 0.13 -0.03 0.06
AdvBookDays -0.24 1.00 0.00 0.00 0.01 0.01
FlyingTime 0.31 0.00 1.00 0.03 0.07 0.20
SeatPitch 0.13 0.00 0.03 1.00 0.54 0.06
SeatWidth -0.03 0.01 0.07 0.54 1.00 0.32
Capacity 0.06 0.01 0.20 0.06 0.32 1.00
Visualizing Correlation
PART 2: LINEAR OLS REGRESSION ANALYSIS
Regression Equation
\( Price = \beta_0 \\ + \beta_1 * AdvBookDays + \beta_2 * Departure + \beta_3 * Weekend \\ + \beta_4 * Diwali + \beta_{5i} * Fly + \beta_{6j} * Airline + \beta_7 * FlyingTime \\ + \beta_8 * SeatPitch + \beta_9 * SeatWidth \\ + \beta_{10} * AdvBookdays * Departure \\ + \beta_{11} * AdvBookDays * Weekend \\ + \beta_{12} * AdvBookDays * Diwali + \beta_{13i} * AdvBookDays * Fly \\ + \beta_{14j} * AdvBookDays * Airline \\ + \beta_{15} * AdvBookDays * FlyingTime \\ + \epsilon \)
where
- Fly {i = 0,1,2,3}
- 0: MM
- 1: MN
- 2: NM
- 3: NN
- Airline {j = 0,1,2,3}
- 0: Air India
- 1: IndiGo
- 2: Jet Airways
- 3: Spice Jet
Call:
lm(formula = Price ~ AdvBookDays + Departure * AdvBookDays +
Weekend * AdvBookDays + Diwali * AdvBookDays + Fly * AdvBookDays +
Airline * AdvBookDays + FlyingTime * AdvBookDays + SeatPitch +
SeatWidth, data = airlineData.df)
Residuals:
Min 1Q Median 3Q Max
-5931.4 -1404.3 -487.2 651.4 13604.7
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.792e+03 1.098e+03 1.633 0.102586
AdvBookDays -9.322e+01 1.471e+01 -6.338 2.46e-10 ***
DeparturePM -2.828e+02 1.060e+02 -2.667 0.007673 **
WeekendYes -4.176e+02 1.152e+02 -3.625 0.000291 ***
DiwaliYes -1.732e+03 4.551e+02 -3.807 0.000142 ***
FlyMN -7.168e+02 1.647e+02 -4.353 1.36e-05 ***
FlyNM -8.315e+02 1.612e+02 -5.159 2.54e-07 ***
FlyNN -1.101e+03 1.778e+02 -6.189 6.33e-10 ***
AirlineIndiGo -1.196e+03 1.610e+02 -7.430 1.20e-13 ***
AirlineJet Airways -3.383e+02 1.579e+02 -2.143 0.032167 *
AirlineSpice Jet -1.025e+03 1.845e+02 -5.558 2.81e-08 ***
FlyingTime 3.197e+01 1.437e+00 22.247 < 2e-16 ***
SeatPitch -3.967e+01 3.720e+01 -1.066 0.286317
SeatWidth 2.316e+02 9.395e+01 2.465 0.013714 *
AdvBookDays:DeparturePM 1.573e+01 6.032e+00 2.608 0.009135 **
AdvBookDays:WeekendYes 2.261e+01 9.262e+00 2.441 0.014680 *
AdvBookDays:DiwaliYes 8.927e+01 2.616e+01 3.412 0.000648 ***
AdvBookDays:FlyMN 6.710e+01 9.302e+00 7.214 5.93e-13 ***
AdvBookDays:FlyNM 4.867e+01 9.121e+00 5.336 9.75e-08 ***
AdvBookDays:FlyNN 6.217e+01 1.008e+01 6.171 7.13e-10 ***
AdvBookDays:AirlineIndiGo -1.921e+01 8.117e+00 -2.366 0.017986 *
AdvBookDays:AirlineJet Airways 7.090e+00 8.776e+00 0.808 0.419157
AdvBookDays:AirlineSpice Jet -2.316e+01 1.013e+01 -2.286 0.022272 *
AdvBookDays:FlyingTime -2.802e-01 8.166e-02 -3.431 0.000605 ***
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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2338 on 8091 degrees of freedom
Multiple R-squared: 0.268, Adjusted R-squared: 0.2659
F-statistic: 128.8 on 23 and 8091 DF, p-value: < 2.2e-16
Beta Coefficients
coefficients(fitOLSIntModel)
(Intercept) 1791.8415106
AdvBookDays -93.2208420
DeparturePM -282.7564058
WeekendYes -417.5691687
DiwaliYes -1732.3204978
FlyMN -716.7920486
FlyNM -831.4731348
FlyNN -1100.6805409
AirlineIndiGo -1195.9108860
AirlineJet Airways -338.2668748
AirlineSpice Jet -1025.2912149
FlyingTime 31.9717342
SeatPitch -39.6693967
SeatWidth 231.6157136
AdvBookDays:DeparturePM 15.7302382
AdvBookDays:WeekendYes 22.6057773
AdvBookDays:DiwaliYes 89.2650908
AdvBookDays:FlyMN 67.1009701
AdvBookDays:FlyNM 48.6683588
AdvBookDays:FlyNN 62.1709674
AdvBookDays:AirlineIndiGo -19.2091229
AdvBookDays:AirlineJet Airways 7.0902634
AdvBookDays:AirlineSpice Jet -23.1624717
AdvBookDays:FlyingTime -0.2801493
Visualizing Beta Coefficients All Predictors
Visualizing Beta Coefficients (selected range)
Log-Linear Model
Regression Equation
\( log(Price) = \beta_0 \\ + \beta_1 * AdvBookDays + \beta_2 * Departure + \beta_3 * Weekend \\ + \beta_4 * Diwali + \beta_{5i} * Fly + \beta_{6j} * Airline + \beta_7 * FlyingTime \\ + \beta_8 * SeatPitch + \beta_9 * SeatWidth \\ + \beta_{10} * AdvBookdays * Departure \\ + \beta_{11} * AdvBookDays * Weekend \\ + \beta_{12} * AdvBookDays * Diwali + \beta_{13i} * AdvBookDays * Fly \\ + \beta_{14j} * AdvBookDays * Airline \\ + \beta_{15} * AdvBookDays * FlyingTime \\ + \epsilon \)
where
- Fly {i = 0,1,2,3}
- 0: MM
- 1: MN
- 2: NM
- 3: NN
- Airline {j = 0,1,2,3}
- 0: Air India
- 1: IndiGo
- 2: Jet Airways
- 3: Spice Jet
Call:
lm(formula = log(Price) ~ AdvBookDays + Departure * AdvBookDays +
Weekend * AdvBookDays + Diwali * AdvBookDays + Fly * AdvBookDays +
Airline * AdvBookDays + FlyingTime * AdvBookDays + SeatPitch +
SeatWidth, data = airlineData.df)
Residuals:
Min 1Q Median 3Q Max
-2.20262 -0.23681 -0.03116 0.19015 1.50670
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.842e+00 1.811e-01 43.312 < 2e-16 ***
AdvBookDays -2.065e-02 2.426e-03 -8.509 < 2e-16 ***
DeparturePM -2.799e-02 1.749e-02 -1.600 0.109636
WeekendYes -5.855e-02 1.900e-02 -3.081 0.002071 **
DiwaliYes -3.789e-01 7.507e-02 -5.047 4.58e-07 ***
FlyMN -9.837e-02 2.716e-02 -3.621 0.000295 ***
FlyNM -1.214e-01 2.659e-02 -4.567 5.02e-06 ***
FlyNN -1.881e-01 2.934e-02 -6.411 1.52e-10 ***
AirlineIndiGo -1.804e-01 2.655e-02 -6.794 1.17e-11 ***
AirlineJet Airways -2.195e-02 2.604e-02 -0.843 0.399451
AirlineSpice Jet -1.207e-01 3.043e-02 -3.965 7.40e-05 ***
FlyingTime 5.547e-03 2.371e-04 23.399 < 2e-16 ***
SeatPitch -1.485e-02 6.137e-03 -2.419 0.015589 *
SeatWidth 5.309e-02 1.550e-02 3.425 0.000617 ***
AdvBookDays:DeparturePM 2.135e-03 9.951e-04 2.145 0.031979 *
AdvBookDays:WeekendYes 5.068e-03 1.528e-03 3.317 0.000914 ***
AdvBookDays:DiwaliYes 1.891e-02 4.316e-03 4.381 1.19e-05 ***
AdvBookDays:FlyMN 1.006e-02 1.534e-03 6.555 5.89e-11 ***
AdvBookDays:FlyNM 6.608e-03 1.505e-03 4.392 1.14e-05 ***
AdvBookDays:FlyNN 8.334e-03 1.662e-03 5.014 5.44e-07 ***
AdvBookDays:AirlineIndiGo -6.380e-03 1.339e-03 -4.764 1.93e-06 ***
AdvBookDays:AirlineJet Airways -1.443e-04 1.448e-03 -0.100 0.920608
AdvBookDays:AirlineSpice Jet -8.245e-03 1.671e-03 -4.933 8.26e-07 ***
AdvBookDays:FlyingTime 1.328e-05 1.347e-05 0.986 0.324177
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.3858 on 8091 degrees of freedom
Multiple R-squared: 0.3522, Adjusted R-squared: 0.3503
F-statistic: 191.2 on 23 and 8091 DF, p-value: < 2.2e-16
Beta Coefficients
coefficients(olslog)
(Intercept) 7.8417917266
AdvBookDays -0.0206467641
DeparturePM -0.0279856827
WeekendYes -0.0585456582
DiwaliYes -0.3789070710
FlyMN -0.0983678610
FlyNM -0.1214227182
FlyNN -0.1880866635
AirlineIndiGo -0.1804079674
AirlineJet Airways -0.0219450455
AirlineSpice Jet -0.1206583509
FlyingTime 0.0055473895
SeatPitch -0.0148452011
SeatWidth 0.0530902046
AdvBookDays:DeparturePM 0.0021346370
AdvBookDays:WeekendYes 0.0050682676
AdvBookDays:DiwaliYes 0.0189086305
AdvBookDays:FlyMN 0.0100589528
AdvBookDays:FlyNM 0.0066077998
AdvBookDays:FlyNN 0.0083339959
AdvBookDays:AirlineIndiGo -0.0063796717
AdvBookDays:AirlineJet Airways -0.0001442955
AdvBookDays:AirlineSpice Jet -0.0082448089
AdvBookDays:FlyingTime 0.0000132815
INTERACTION PLOTS
Interaction plot of Advance Booking Days and Departure Time
Interaction plot of Advance Booking Days and Weekend
Interaction plot of Advance Booking Days and Diwali
Interaction plot of Advance Booking Days and Departure-Arrival City
Interaction plot of Advance Booking Days and Flying Time
Interaction plot of Advance Booking Days and Airline
Expected Ticket Prices for (AM vs PM, Weekday, Non-Diwali)
Air India IndiGo Jet Airways Spice Jet
MM 5830.57 4433.18 5691.95 4579.12
MN 6124.57 4656.72 5978.96 4810.02
NM 5689.52 4325.94 5554.25 4468.35
NN 5459.11 4150.75 5329.32 4287.39
Air India IndiGo Jet Airways Spice Jet
MM 5850.01 4447.97 5710.93 4594.39
MN 6144.99 4672.25 5998.90 4826.06
NM 5708.49 4340.37 5572.78 4483.25
NN 5477.31 4164.59 5347.09 4301.68
Expected Price Difference between PM and AM Departure Flights
Air India IndiGo Jet Airways Spice Jet
MM 19.44 14.79 18.98 15.27
MN 20.42 15.53 19.94 16.04
NM 18.97 14.43 18.53 14.90
NN 18.20 13.84 17.77 14.29
Expected Ticket Prices for (AM, Weekday vs Weekend, Non-Diwali)
Air India IndiGo Jet Airways Spice Jet
MM 5830.57 4433.18 5691.95 4579.12
MN 6124.57 4656.72 5978.96 4810.02
NM 5689.52 4325.94 5554.25 4468.35
NN 5459.11 4150.75 5329.32 4287.39
Air India IndiGo Jet Airways Spice Jet
MM 5923.45 4503.80 5782.62 4652.06
MN 6222.13 4730.91 6074.21 4886.64
NM 5780.16 4394.85 5642.73 4539.53
NN 5546.07 4216.87 5414.21 4355.69
Expected Price Difference between Weekend and Weekday Tickets
Air India IndiGo Jet Airways Spice Jet
MM 92.88 70.62 90.67 72.94
MN 97.56 74.19 95.25 76.62
NM 90.64 68.91 88.48 71.18
NN 86.96 66.12 84.89 68.30
Expected Ticket Prices for (AM, Weekday, Non-Diwali vs. Diwali)
Air India IndiGo Jet Airways Spice Jet
MM 5830.57 4433.18 5691.95 4579.12
MN 6124.57 4656.72 5978.96 4810.02
NM 5689.52 4325.94 5554.25 4468.35
NN 5459.11 4150.75 5329.32 4287.39
Air India IndiGo Jet Airways Spice Jet
MM 5267.69 4005.21 5142.45 4137.05
MN 5533.31 4207.17 5401.76 4345.66
NM 5140.26 3908.32 5018.05 4036.98
NN 4932.09 3750.04 4814.83 3873.49
Expected Price Difference between Diwali and Non-Diwali Tickets
Air India IndiGo Jet Airways Spice Jet
MM -562.88 -427.97 -549.50 -442.07
MN -591.26 -449.55 -577.20 -464.36
NM -549.26 -417.62 -536.20 -431.37
NN -527.02 -400.71 -514.49 -413.90