MSCI 3230 Final Project - Airline Data Analysis
Filip Dragicevic1
1 Introduction & Preprocessing
1.1 Objective:
1.2 Summary:
1.2.1 - By completing & analyzing the summary of the dataset, we can quickly observe values such as maximum, minimum, mean & median, quartiles, and number of missing values for all numeric columns. Since string values such as type, class, and cancellation are factors with a limited number of possible outputs, the summary tab displays the count of each of the values, as seen below.
> summary(airline) Satisfaction Status Age Gender No.Flights
Min. :1.000 Blue :1304 Min. :15.00 Female:1035 Min. : 1.00
1st Qu.:3.000 Gold : 161 1st Qu.:34.00 Male : 862 1st Qu.:10.00
Median :4.000 Platinum: 57 Median :46.00 Median :18.00
Mean :3.396 Silver : 375 Mean :46.92 Mean :20.82
3rd Qu.:4.000 3rd Qu.:59.00 3rd Qu.:29.00
Max. :5.000 Max. :85.00 Max. :84.00
Type Shopping Eating Class
Business travel:1181 Min. : 0.00 Min. : 0.0 Business: 152
Mileage tickets: 153 1st Qu.: 0.00 1st Qu.: 30.0 Eco :1552
Personal Travel: 563 Median : 0.00 Median : 60.0 Eco Plus: 193
Mean : 26.22 Mean : 68.5
3rd Qu.: 30.00 3rd Qu.: 90.0
Max. :364.00 Max. :440.0
Dep.Delay Arr.Delay Cancel Time Distance
Min. : 0.00 Min. : 0.00 No :1860 Min. : 17.00 Min. : 67.0
1st Qu.: 0.00 1st Qu.: 0.00 Yes: 37 1st Qu.: 32.00 1st Qu.: 158.0
Median : 0.00 Median : 0.00 Median : 48.00 Median : 282.0
Mean : 11.67 Mean : 13.39 Mean : 56.25 Mean : 352.3
3rd Qu.: 9.00 3rd Qu.: 12.00 3rd Qu.: 64.25 3rd Qu.: 408.0
Max. :423.00 Max. :417.00 Max. :169.00 Max. :1250.0
NA's :34 NA's :37 NA's :37 1.3 Missing Values:
1.3.1 - By creating a table using the ‘is.na’ function, we are able to see that the airline dataset contains 108 missing values (from the departure delay, arrival delay, and flight time columns) denoted as N/A. We will replace them with the mean values for each given category.
> table(is.na(airline))
FALSE TRUE
26450 108 > airline$Dep.Delay[is.na(airline$Dep.Delay)] <- mean(airline$Dep.Delay, na.rm = TRUE)
> airline$Arr.Delay[is.na(airline$Arr.Delay)] <- mean(airline$Arr.Delay, na.rm = TRUE)
> airline$Time[is.na(airline$Time)] <- mean(airline$Time, na.rm = TRUE)
> airline$No.Flights[is.na(airline$No.Flights)] <- mean(airline$No.Flights, na.rm = TRUE)
> table(is.na(airline))
FALSE
26558 1.4 Data Partitioning:
1.4.1 - Partitioning is the process of spliting the dataset into testing and training. For our dataset, we will be using a split of 0.7.
> library(caTools)Warning: package 'caTools' was built under R version 4.1.3> split = sample.split(airline, SplitRatio = 0.7)
> training_set = subset(airline, split == 'True')
> test_set = subset(airline, split == 'False')
> training_set [1] Satisfaction Status Age Gender No.Flights
[6] Type Shopping Eating Class Dep.Delay
[11] Arr.Delay Cancel Time Distance
<0 rows> (or 0-length row.names)> test_set [1] Satisfaction Status Age Gender No.Flights
[6] Type Shopping Eating Class Dep.Delay
[11] Arr.Delay Cancel Time Distance
<0 rows> (or 0-length row.names)1.5 Data Modification:
1.5.1 - We will also be creating a new dataframe that removes zero values, as the number of outliers and de-standardized values is far too high for any linear regression models.
> head(df1, n = 5) Satisfaction Status Age Gender No.Flights Type Shopping Eating
1 5 Silver 32 Male 1 Business travel 10 46
2 2 Blue 66 Male 1 Personal Travel 255 335
3 3 Blue 28 Female 1 Business travel 30 70
4 3 Blue 50 Female 1 Personal Travel 15 60
5 4 Silver 46 Female 1 Business travel 120 150
Class Dep.Delay Arr.Delay Cancel Time Distance
1 Eco 66 61 No 43 227
2 Eco 55 59 No 44 227
3 Eco 15 21 No 27 140
4 Eco 10 2 No 97 772
5 Eco 2 16 No 113 9871.5.2 - The new dataframe consists of 241 observations with the same 14 columns. By creating this dataframe, we will be able to conduct data useful data visualization and predictive analysis, as the data is more standardized and far less skewed to the lower values.
> summary(df1) Satisfaction Status Age Gender
Min. :1.000 Length:241 Min. :15.00 Length:241
1st Qu.:2.000 Class :character 1st Qu.:36.00 Class :character
Median :3.000 Mode :character Median :46.00 Mode :character
Mean :3.344 Mean :48.27
3rd Qu.:4.000 3rd Qu.:62.00
Max. :5.000 Max. :85.00
No.Flights Type Shopping Eating
Min. : 1.00 Length:241 Min. : 2.00 Min. : 8.00
1st Qu.:10.00 Class :character 1st Qu.: 20.00 1st Qu.: 40.00
Median :19.00 Mode :character Median : 45.00 Median : 65.00
Mean :19.44 Mean : 60.85 Mean : 79.44
3rd Qu.:26.00 3rd Qu.: 85.00 3rd Qu.:105.00
Max. :58.00 Max. :344.00 Max. :390.00
Class Dep.Delay Arr.Delay Cancel
Length:241 Min. : 1.00 Min. : 1.00 Length:241
Class :character 1st Qu.: 11.00 1st Qu.: 12.00 Class :character
Mode :character Median : 27.00 Median : 26.00 Mode :character
Mean : 37.11 Mean : 40.07
3rd Qu.: 47.00 3rd Qu.: 52.00
Max. :212.00 Max. :293.00
Time Distance
Min. : 18.00 Min. : 89.0
1st Qu.: 37.00 1st Qu.: 164.0
Median : 49.00 Median : 293.0
Mean : 58.84 Mean : 368.8
3rd Qu.: 72.00 3rd Qu.: 482.0
Max. :144.00 Max. :1250.0 2 Data Visualization
2.0.1 - Data visualization consists of creating graphical representations of the data. Using charts, graphs, maps, etc., it is used to get a better understanding of trends and patterns in the data, without having to do any initial statistical analysis. From these visualizations, we can make quick interpretations and insights that can be built upon using further methods & models. For our airlines dataset, we will be creating several histograms, box & whisker plots, scatterplots, matricies, and more.
2.1 Satisfaction Histogram:
> with(df1, Hist(Satisfaction, scale="frequency", breaks=3,
+ col="tomato"))
2.1.1 - Based on the histogram, the satisfaction data looks to be slightly left-skewed, as the tail on the left side is longer than the right side. To confirm these results, we can run a test of normality.
2.2 Satisfaction Normality Test:
2.2.1 - The test of normality is used to determine whether a sample in a given dataset is normally distributed and can further be used for linear regression models. For our dataset, satisfaction is the main output we are going to analyze, which will be done using the Shapiro-Wilk test.
> normalityTest(~Satisfaction, test="shapiro.test", data=df1)
Shapiro-Wilk normality test
data: Satisfaction
W = 0.90087, p-value = 1.622e-112.2.2 - Since the p-value is less than 0.05, we reject the standard null-hypothesis that the data is normally distributed, confirming that it is not normally distributed. As a result, it should be transformed to remove skew and better prepare it for linear regression models.
> skewness(df1$Satisfaction)[1] -0.12089482.2.3 - The skewness value of the satisfaction column is -0.1210
> powerTransform(df1$Satisfaction)Estimated transformation parameter
df1$Satisfaction
1.008903 2.2.4 - The powerTransform function relatively explains how to transform non-normal distribution into normal.
> Sat <- (df1$Satisfaction)^1.22.2.5 - As a result, we will square the data by 1.2 in hopes of increasing the skewness value and bringing it closer to 0 (normal).
> skewness(Sat)[1] -0.0074166732.2.6 - The new skewness value is -0.007, much closer to zero than the original value
> hist(Sat, breaks = 3, col = 'tomato')
2.2.7 - This can also be seen by the new histogram, which is much more evenly distributed. As a result, create a new column in the dataset named ‘Sat’ for further use in linear regression models.
2.3 Barplots:
> with(df1, Barplot(Type, xlab="Type", ylab="Frequency", label.bars=TRUE, col="plum"))
2.3.1 - This barplot shows that business travel (159) is the most common type, followed by personal (71), and mileage tickets (11)
> with(df1, Barplot(Status, xlab="Status", ylab="Frequency",
+ label.bars=TRUE, col="plum"))
2.3.2 - This barplot shows that blue (159) is the most common status, followed by silver (53), gold (25), and platinum (11)
> with(df1, Barplot(Gender, xlab="Gender", ylab="Frequency",
+ label.bars=TRUE, col="plum"))
2.3.3 - This barplot shows that there are more female flyers (136) then male (105)
> with(df1, Barplot(Class, xlab="Class", ylab="Frequency",
+ label.bars=TRUE, col="plum"))
2.3.4 - This barplot shows that the eco class (192) is the most common, followed by eco plus (28) and business (21)
2.4 Boxplots:
> Boxplot( ~ Distance, data=df1, id=list(method="y"), col="palegreen")
[1] "5" "17" "48" "72" "147" "161" "206"2.4.1 - The distance boxplot shows that it has a positive skew, as most of the data is above the median, with several outliers above the max value.
> Boxplot( ~ Time, data=df1, id=list(method="y"), col="palegreen")
[1] "27" "35" "48" "49" "72" "91" "161" "178" "206"2.4.2 - The time boxplot shows that it has a positive skew, as most of the data is above the median, with several outliers above the max value.
> Boxplot( ~ Arr.Delay, data=df1, id=list(method="y"), col="palegreen")
[1] "199" "218" "23" "134" "22" "109" "130" "189" "229" "64" 2.4.3 - The arrival delay boxplot shows that it has a positive skew, as most of the data is above the median, with several outliers above the max value.
> Boxplot( ~ Dep.Delay, data=df1, id=list(method="y"), col="palegreen")
[1] "134" "22" "199" "130" "218" "23" "109" "189" "229" "42" 2.4.4 - The departure delay boxplot shows that it has a positive skew, as most of the data is above the median, with several outliers above the max value.
> Boxplot( ~ Eating, data=df1, id=list(method="y"), col="palegreen")
[1] "2" "34" "43" "79" "133" "158" "196" "222" "230"2.4.5 - The eating boxplot shows that it has a positive skew, as most of the data is above the median, with several outliers above the max value.
> Boxplot( ~ Shopping, data=df1, id=list(method="y"), col="palegreen")
[1] "13" "123" "7" "2" "119" "103" "127" "154" "85" "23" 2.4.6 - The shopping boxplot shows that it has a positive skew, as most of the data is above the median, with several outliers above the max value.
> scatterplot(Time~Distance, regLine=FALSE, smooth=FALSE, boxplots=FALSE,
+ data=df1)
2.5 Scatterplots:
2.5.1 - Time and distance are positively correlated; the greater the flight distance, the more time it takes.
> scatterplot(Dep.Delay~Arr.Delay, regLine=FALSE, smooth=FALSE,
+ boxplots=FALSE, data=df1)
2.5.2 - Similarly, as departure delay increases, as does the arrival delay.
> scatterplot(Arr.Delay~Distance, regLine=FALSE, smooth=FALSE, boxplots=FALSE,
+ data=df1)
2.5.3 - As flight distance increases, the arrival delay decreases, meaning they are negatively correlated.
> scatterplot(Dep.Delay~Distance, regLine=FALSE, smooth=FALSE, boxplots=FALSE,
+ data=df1)
2.5.4 - Similarly, as flight distance increases, the departure delay also decreases.
> scatterplot(Eating~Age, regLine=FALSE, smooth=FALSE, boxplots=FALSE,
+ data=df1)
> scatterplot(Shopping~Age, regLine=FALSE, smooth=FALSE, boxplots=FALSE,
+ data=df1)
2.5.5 - Although there are not distinct patterns, ages from 30-50 have more occurences of shopping and eating at the airport.
2.6 Correlation Matrix:
> cor(df1[,c("Age","Arr.Delay","Dep.Delay","Distance","Eating","No.Flights",
+ "Satisfaction","Shopping","Time")], use="complete") Age Arr.Delay Dep.Delay Distance Eating
Age 1.000000000 0.02860769 0.01428243 0.10304631 0.128048283
Arr.Delay 0.028607686 1.00000000 0.94982706 -0.02218009 0.040647718
Dep.Delay 0.014282427 0.94982706 1.00000000 -0.08909600 0.043504654
Distance 0.103046310 -0.02218009 -0.08909600 1.00000000 0.001800230
Eating 0.128048283 0.04064772 0.04350465 0.00180023 1.000000000
No.Flights 0.262497538 -0.03899427 -0.03284574 -0.10728595 -0.056043596
Satisfaction -0.388650992 -0.11575043 -0.09016724 -0.08272827 0.087443017
Shopping 0.007733124 0.08167980 0.09208845 0.01222653 0.100650875
Time 0.134453426 0.06785729 -0.03419199 0.96282207 0.004430232
No.Flights Satisfaction Shopping Time
Age 0.26249754 -0.388650992 0.007733124 0.134453426
Arr.Delay -0.03899427 -0.115750433 0.081679803 0.067857290
Dep.Delay -0.03284574 -0.090167239 0.092088452 -0.034191989
Distance -0.10728595 -0.082728268 0.012226529 0.962822068
Eating -0.05604360 0.087443017 0.100650875 0.004430232
No.Flights 1.00000000 -0.230368647 -0.161056860 -0.108591501
Satisfaction -0.23036865 1.000000000 -0.001115951 -0.117144434
Shopping -0.16105686 -0.001115951 1.000000000 0.013178219
Time -0.10859150 -0.117144434 0.013178219 1.0000000002.6.2 - As age increases, satisfaction decreases (-0.3887)
2.6.3 - As number of flights increases, satisfaction decreases (-0.2304)
2.6.4 - As arrival delay increases, satisfaction decreases (-0.1158)
2.6.5 - As eating increases, satisfaction increases (0.0874)
3 Predictive Analysis
3.0.1 - When undergoing predictive analysis, models are used to analyze trends and patterns of future outcomes based on historical data. In our dataset, satisfaction is the main output that we are going to predict using the other inputs as determinants. These results will then be presented to upper management in a professional report to assist and guide them to make better future decisions regarding customer airline satisfaction.
3.1 Dummy Variables:
3.1.1 - When using dummy variables in linear regression, always choose 1 less than ‘n’ in your model and use the other as a benchmark.
> df1$ifBusinessClass <- with(df1, ifelse(Class=="Business",1,0))> df1$ifEcoClass <- with(df1, ifelse(Class=="Eco",1,0))> df1$ifFemale <- with(df1, ifelse(Gender=="Female",1,0))> df1$ifSilver <- with(df1, ifelse(Status=="Silver",1,0))> df1$ifGold <- with(df1, ifelse(Status=="Gold",1,0))> df1$ifPlatinum <- with(df1, ifelse(Status=="Platinum",1,0))> df1$ifBusinessTravel <- with(df1, ifelse(Type=="Business travel",1,0))> df1$ifPersonalTravel <- with(df1, ifelse(Type=="Personal Travel",1,0))3.2 Dummy Variables Model:
3.2.1 - After creating all dummy variables, we can run a linear regression model using just these variables to get a better understanding of them and how they behave with one another, as well as the satisfaction itself.
> RegModel.1 <-
+ lm(Satisfaction~ifBusinessClass+ifBusinessTravel+ifEcoClass+ifFemale+ifGold+ifPersonalTravel+ifPlatinum+ifSilver,
+ data=df1)
> summary(RegModel.1)
Call:
lm(formula = Satisfaction ~ ifBusinessClass + ifBusinessTravel +
ifEcoClass + ifFemale + ifGold + ifPersonalTravel + ifPlatinum +
ifSilver, data = df1)
Residuals:
Min 1Q Median 3Q Max
-2.37695 -0.37695 -0.02631 0.47610 2.97369
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.5183 0.2940 11.966 < 2e-16 ***
ifBusinessClass 0.1595 0.2279 0.700 0.48487
ifBusinessTravel 0.2341 0.2444 0.958 0.33923
ifEcoClass -0.2285 0.1594 -1.433 0.15315
ifFemale -0.1469 0.1029 -1.428 0.15462
ifGold 0.5057 0.1679 3.012 0.00288 **
ifPersonalTravel -1.1165 0.2537 -4.401 1.64e-05 ***
ifPlatinum 1.1198 0.2443 4.584 7.47e-06 ***
ifSilver 0.6734 0.1260 5.343 2.18e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.7747 on 232 degrees of freedom
Multiple R-squared: 0.5035, Adjusted R-squared: 0.4864
F-statistic: 29.41 on 8 and 232 DF, p-value: < 2.2e-16> confint(RegModel.1) 2.5 % 97.5 %
(Intercept) 2.9389833 4.09754747
ifBusinessClass -0.2895953 0.60850060
ifBusinessTravel -0.2475090 0.71568691
ifEcoClass -0.5425296 0.08561130
ifFemale -0.3496712 0.05578752
ifGold 0.1748751 0.83647243
ifPersonalTravel -1.6163612 -0.61673859
ifPlatinum 0.6384887 1.60118727
ifSilver 0.4251043 0.921786963.2.2 - Business Class is expected to have a higher satisfaction by 0.1595 compared to Eco Plus. Eco is expected to have a lower satisfaction by -0.2285 compared to Eco Plus.
3.2.3 - Business Travel is expected to have a higher satisfaction by 0.2341 compared to Mileage Tickets. Personal travel is expected to have a lower satisfaction by -1.1165 compared to Mileage Tickets.
3.2.4 - Female is expected to have a lower satisfaction by -0.1469 than male.
3.2.5 - Compared to Blue fliers, Gold is expected to have a higher satisfaction by 0.5057, Silver by 0.6734, and Platinum by 1.1198.
3.2.6 - Based on the Adjusted R-Squared value of 0.4864, we can conclude that using these inputs to determine satisfaction returns a weak model, and that is not very useful for upper management.
3.3 All Variables Model:
> RegModel.3 <-
+ lm(Satisfaction~Age+Arr.Delay+Dep.Delay+Distance+Eating+ifBusinessClass+ifBusinessTravel+ifEcoClass+ifFemale+ifGold+ifPersonalTravel+ifPlatinum+ifSilver+No.Flights+Shopping+Time,
+ data=df1)
> summary(RegModel.3)
Call:
lm(formula = Satisfaction ~ Age + Arr.Delay + Dep.Delay + Distance +
Eating + ifBusinessClass + ifBusinessTravel + ifEcoClass +
ifFemale + ifGold + ifPersonalTravel + ifPlatinum + ifSilver +
No.Flights + Shopping + Time, data = df1)
Residuals:
Min 1Q Median 3Q Max
-2.2788 -0.4389 0.0099 0.4647 2.4056
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.129e+00 3.497e-01 11.806 < 2e-16 ***
Age -1.104e-02 3.358e-03 -3.289 0.001169 **
Arr.Delay -6.424e-03 4.169e-03 -1.541 0.124802
Dep.Delay 5.722e-03 4.701e-03 1.217 0.224788
Distance 9.223e-07 8.112e-04 0.001 0.999094
Eating 1.949e-03 9.004e-04 2.164 0.031491 *
ifBusinessClass 2.134e-01 2.214e-01 0.964 0.336066
ifBusinessTravel 1.835e-01 2.417e-01 0.759 0.448720
ifEcoClass -2.388e-01 1.539e-01 -1.551 0.122236
ifFemale -1.212e-01 1.038e-01 -1.168 0.244164
ifGold 5.956e-01 1.659e-01 3.589 0.000407 ***
ifPersonalTravel -1.005e+00 2.576e-01 -3.899 0.000127 ***
ifPlatinum 1.008e+00 2.400e-01 4.198 3.89e-05 ***
ifSilver 6.456e-01 1.246e-01 5.179 4.96e-07 ***
No.Flights -2.427e-03 4.533e-03 -0.535 0.592837
Shopping 3.355e-05 8.584e-04 0.039 0.968864
Time -2.574e-03 6.787e-03 -0.379 0.704901
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.7456 on 224 degrees of freedom
Multiple R-squared: 0.5559, Adjusted R-squared: 0.5242
F-statistic: 17.52 on 16 and 224 DF, p-value: < 2.2e-163.3.1 - We can then run a linear regression model using all variables existing & created, as a test run before choosing the best model. From this model, we can see that the Adjusted R-Squared value went up to 0.5242, and that the p-value is less than our benchmark of 0.05. As this model contains all of our variables and has an R-Squared value of 0.5242, we can conclude that this is the best overall model for our predictive analysis, and that it will be useful for upper managements future decisions making process. Having said, we can further analyze the relationships and usefulness of the variables themselves.
3.4 Best Subsets Regression:
3.4.1 - To expand further, we can create two more models in which we split the variables and see which are the best predictors based on the ‘best subsets regression.’
> RegModel.4 <-
+ lm(Satisfaction~Age+Arr.Delay+Distance+Eating+ifGold+ifPersonalTravel+Shopping+Time,
+ data=df1)
> summary(RegModel.4)
Call:
lm(formula = Satisfaction ~ Age + Arr.Delay + Distance + Eating +
ifGold + ifPersonalTravel + Shopping + Time, data = df1)
Residuals:
Min 1Q Median 3Q Max
-2.61440 -0.51768 0.05178 0.46480 2.32185
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.283e+00 2.071e-01 20.686 < 2e-16 ***
Age -1.358e-02 3.525e-03 -3.854 0.00015 ***
Arr.Delay -1.482e-03 1.254e-03 -1.181 0.23870
Distance 6.001e-04 8.111e-04 0.740 0.46013
Eating 3.072e-03 9.467e-04 3.245 0.00135 **
ifGold 3.819e-01 1.738e-01 2.197 0.02899 *
ifPersonalTravel -1.302e+00 1.242e-01 -10.487 < 2e-16 ***
Shopping 7.112e-05 9.024e-04 0.079 0.93725
Time -5.940e-03 6.609e-03 -0.899 0.36968
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.8108 on 232 degrees of freedom
Multiple R-squared: 0.456, Adjusted R-squared: 0.4373
F-statistic: 24.31 on 8 and 232 DF, p-value: < 2.2e-16> best <- ols_step_best_subset(RegModel.4)
> best Best Subsets Regression
----------------------------------------------------------------------------------
Model Index Predictors
----------------------------------------------------------------------------------
1 ifPersonalTravel
2 Age ifPersonalTravel
3 Age Eating ifPersonalTravel
4 Age Eating ifGold ifPersonalTravel
5 Age Arr.Delay Eating ifGold ifPersonalTravel
6 Age Arr.Delay Eating ifGold ifPersonalTravel Time
7 Age Arr.Delay Distance Eating ifGold ifPersonalTravel Time
8 Age Arr.Delay Distance Eating ifGold ifPersonalTravel Shopping Time
----------------------------------------------------------------------------------
Subsets Regression Summary
----------------------------------------------------------------------------------------------------------------------------------
Adj. Pred
Model R-Square R-Square R-Square C(p) AIC SBIC SBC MSEP FPE HSP APC
----------------------------------------------------------------------------------------------------------------------------------
1 0.3842 0.3816 0.374 25.6549 609.6019 -74.6698 620.0563 174.1341 0.7285 0.0030 0.6261
2 0.4135 0.4086 0.398 15.1250 599.8217 -84.3282 613.7609 166.5267 0.6996 0.0029 0.6012
3 0.4389 0.4318 0.418 6.3245 591.1840 -92.6885 608.6080 160.0113 0.6749 0.0028 0.5801
4 0.4480 0.4387 0.422 4.4167 589.2163 -94.4761 610.1250 158.0682 0.6695 0.0028 0.5754
5 0.4535 0.4419 0.424 4.0746 588.8067 -94.7160 613.2002 157.1645 0.6683 0.0028 0.5744
6 0.4547 0.4408 0.422 5.5574 590.2712 -93.1515 618.1496 157.4887 0.6724 0.0028 0.5779
7 0.4560 0.4397 0.418 7.0062 591.6994 -91.6118 623.0626 157.7927 0.6764 0.0028 0.5813
8 0.4560 0.4373 0.413 9.0000 593.6929 -89.5402 628.5409 158.4716 0.6820 0.0028 0.5862
----------------------------------------------------------------------------------------------------------------------------------
AIC: Akaike Information Criteria
SBIC: Sawa's Bayesian Information Criteria
SBC: Schwarz Bayesian Criteria
MSEP: Estimated error of prediction, assuming multivariate normality
FPE: Final Prediction Error
HSP: Hocking's Sp
APC: Amemiya Prediction Criteria > plot(best)
3.4.2 - Based on the first best subsets regression, the best dummy variable predictor is ifPersonalTravel, followed by Age and Eating.
> RegModel.5 <-
+ lm(Satisfaction~Dep.Delay+ifBusinessClass+ifBusinessTravel+ifEcoClass+ifFemale+ifPlatinum+ifSilver+No.Flights,
+ data=df1)
> summary(RegModel.5)
Call:
lm(formula = Satisfaction ~ Dep.Delay + ifBusinessClass + ifBusinessTravel +
ifEcoClass + ifFemale + ifPlatinum + ifSilver + No.Flights,
data = df1)
Residuals:
Min 1Q Median 3Q Max
-2.5086 -0.4495 -0.0388 0.4823 2.7510
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.778997 0.234208 11.87 < 2e-16 ***
Dep.Delay -0.000897 0.001393 -0.64 0.52018
ifBusinessClass 0.233884 0.239246 0.98 0.32930
ifBusinessTravel 1.152673 0.116600 9.89 < 2e-16 ***
ifEcoClass -0.145256 0.166937 -0.87 0.38513
ifFemale -0.176991 0.108978 -1.62 0.10571
ifPlatinum 1.003483 0.257096 3.90 0.00012 ***
ifSilver 0.629273 0.129992 4.84 2.4e-06 ***
No.Flights -0.007755 0.004678 -1.66 0.09876 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.813 on 232 degrees of freedom
Multiple R-squared: 0.454, Adjusted R-squared: 0.435
F-statistic: 24.1 on 8 and 232 DF, p-value: <2e-16> best2 <- ols_step_best_subset(RegModel.5)
> best2 Best Subsets Regression
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Model Index Predictors
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1 ifBusinessTravel
2 ifBusinessTravel ifSilver
3 ifBusinessTravel ifPlatinum ifSilver
4 ifBusinessClass ifBusinessTravel ifPlatinum ifSilver
5 ifBusinessClass ifBusinessTravel ifPlatinum ifSilver No.Flights
6 ifBusinessClass ifBusinessTravel ifFemale ifPlatinum ifSilver No.Flights
7 ifBusinessClass ifBusinessTravel ifEcoClass ifFemale ifPlatinum ifSilver No.Flights
8 Dep.Delay ifBusinessClass ifBusinessTravel ifEcoClass ifFemale ifPlatinum ifSilver No.Flights
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Subsets Regression Summary
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Adj. Pred
Model R-Square R-Square R-Square C(p) AIC SBIC SBC MSEP FPE HSP APC
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1 0.3440 0.3413 0.333 41.4859 624.8263 -59.6767 635.2807 185.4894 0.7761 0.0032 0.6670
2 0.3886 0.3835 0.373 24.5451 609.8510 -74.5163 623.7902 173.6030 0.7293 0.0030 0.6268
3 0.4307 0.4235 0.41 8.6888 594.6727 -89.2785 612.0966 162.3444 0.6848 0.0029 0.5885
4 0.4400 0.4305 0.414 6.7386 592.7012 -91.0904 613.6100 160.3706 0.6792 0.0028 0.5837
5 0.4451 0.4333 0.415 6.5823 592.5053 -91.1482 616.8989 159.5951 0.6787 0.0028 0.5833
6 0.4508 0.4367 0.415 6.1459 591.9999 -91.4591 619.8783 158.6224 0.6772 0.0028 0.5820
7 0.4525 0.4361 0.414 7.4148 593.2430 -90.0971 624.6062 158.8066 0.6807 0.0028 0.5851
8 0.4535 0.4347 0.411 9.0000 594.8125 -88.4206 629.6605 159.2094 0.6852 0.0029 0.5889
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AIC: Akaike Information Criteria
SBIC: Sawa's Bayesian Information Criteria
SBC: Schwarz Bayesian Criteria
MSEP: Estimated error of prediction, assuming multivariate normality
FPE: Final Prediction Error
HSP: Hocking's Sp
APC: Amemiya Prediction Criteria > plot(best2)
3.4.3 - And based on the second best subsets regression, the best dummy variable predictor is ifBusinessTravel, followed by ifSilver & ifPlatinum.
4 Conclusion
4.0.1 - Based on the predictive analysis and linear regression models, the biggest predictors of customer airline satisfaction are the type of flight, airline status, class, age of the fliers, as well as eating at the airport. For upper managements’ decision making purposes, they should:
4.0.2 - Improve flight quality for those on personal travel flights. Although some airlines focus on business travel with short flight times and distances, it is also important that personal fliers are also satisfied with their services. This may be several different reasons, as there is a fairly substantial difference in flight experience when comparing business and personal.
4.0.3 - Ask themselves why those flying with Blue status have lower satisfaction levels compared to Gold, Silver, and Platinum. Although it may be best for their business model to focus on those with higher airline status, it is important to satisfy new customers just as much as existing.
4.0.4 - Look in to improving flight quality for Eco and EcoPlus fliers, as Business Class is much more satisfied. Determine why older fliers tend to be less satisfied than younger, and finally, try to improve and advertise eating options.
University of Windsor, dragicef@uwindsor.ca↩︎