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This bachelor thesis in applied mathematics and industrial engineering and management investigates which factors that affect the price of tickets in the travel industry. This has been done by performing different multiple linear regression analyses based on the theory from mathematical statistics and econometrics. The analyses has been made with data that has been provided by MTR Express, containing data of departures of 2016 for the main operators in the railway and airline industry. The route that has been analysed is Stockholm - Gothenburg since this is the route where MTR Express has established its business in the railway market in Sweden. The results of the linear regression analysis show that the variables "Days before departure" and the weekday of travel have the most significant impact on the prices for both train and flight tickets. The final models have an explanation degree of 50% for the railway and 51% for the airline industry. The results show many similarities and correlations between the railway and airline industries. Furthermore, some interesting differences between these subindustries appeared in the final regression models and these have been one of the aspects in the discussion. The conclusion of the thesis is that there are several different aspects affecting the price in the travel industry / Detta kandidatexamensarbete inom tillämpad matematik och industriell ekonomi undersöker vilka faktorer som påverkar priset på biljetter i resebranschen. Detta har gjorts genom linjära regressionsanalyser som har baserats på teorier inom matematisk statistik och ekonometri. Dessa analyser har gjorts möjliga med hjälp av data från MTR Express som innehåller information om avgångar under 2016 för de största aktörerna inom tåg- och flygbranschen i Sverige. Den sträcka som analyserats är Stockholm - Göteborg då detta är den rutt som MTR Express har etablerat sig på. Resultatet av de regressionsmodeller som beräknats fram visar att faktorerna "dagar före avresa" och veckodag för avresa har stor påverkan på priset för såväl flyg som tåg. De slutgiltiga modellerna visar en förklaringsgrad på 50 % och 51 % för tåg- respektive flygindustrin. Resultaten visar likheter och korrelation mellan tåg- och flygindustrin. Utöver likheter mellan branscherna har även intressanta skillnader gått att identifiera från resultaten som diskuteras i rapporten. De slutsatser som går att dra från detta kandidatexamensarbete är att det finns många faktorer som påverkar priset på resor men att vissa har större påverkan och bör tas i beaktning när man ska köpa biljetter.

As the software industry grows larger by the minute, the need for automated solutions within bug report management is on the rise. Although some research has been conducted in the area of bug handling, new, faster or more precise approaches are yet to be developed. A bug report typically contains a free text observations field where the issue can be described by a human. Research regarding processing of this type of field is extensive, however, bug reports are often accompanied with system log files which have been given less attention so far. In the 4G LTE telecommunications network, the available system log files are many and several are likely to aid the routing of bug reports. In this thesis, one system log file was chosen to be evaluated; the alarm log. The alarm logs are time series count data containing alarms raised by the system. The alarm log data have been pre-processed with data mining techniques. The Apriori algorithm has been used to mine for specific alarms and alarming objects which indicates that the bug report should be solved by a particular developer group. We extend the Apriori algorithm to a temporal setting by using a customised time dependent confidence measure. To further mine for interesting sequences of events in the logs, the sequence mining approach SPADE has been used. The extracted class-associated sequences from both pre-processing approaches are transformed into binary features possible to use as predictors in any prediction model. The results have been evaluated by predicting the correct developer group with two different methods; logistic regression and DO-probit. Logistic regression was regularised with the elastic net penalty to avoid computational issues as well as handling the sparse covariate set. DO-probit was used with a horseshoe prior; it is well suited for the sparse covariate regression problem as it is customised to obtain signals in sparse, noisy data. The results indicate that a data mining approach for processing alarm logs is promising. The results show that the rules obtained with the Apriori mining process are suitable for mining the alarm logs as most binary representations of the rules used as covariates in logistic regression are kept in the equations for the expected classes with strongly positive coefficients. Although, the overall improvement in accuracy from using the alarms logs in addition to the learned topics from free text fields is modest, the alarm logs are concluded to be a good complement to the free text information as some Apriori covariates appears to be better suited to predict some classes than some topics.

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När  en  fall-kontrollstudie  har  genomförts  kan  det  vara  av  intresse  att  genomföra en sekundär analys som studerar fall-kontrollstudiens utfalls effekt på någon annan variabel i populationen. I dessa fall ses fall-kontrollstudiens utfall som en behandling i sekundäranalysen och denna variabels effekt på ett nytt utfall undersöks. I observationsstudier baserade på fall-kontrolldata existerar ofta systematiska skillnader mellan fall- och kontrollgruppen. Om dessa  skillnader  i  bakgrundsvariabler  mellan  grupperna påverkar  både  behandlingen och utfallet kommer det att skapa bias i skattningen av den kausala effekten. Ett sätt att kontrollera för dessa bakgrundsvariabler är genom att matcha på propensity score. Denna  uppsats  består  av  en  simuleringsstudie  där  den  kausala  effekten  på utfallet för de behandlade skattas med hjälp av propensity score matchning i  en  sekundäranalys  av  matchat  fall-kontrolldata.  Syftet är  att  undersöka matchingsestimatorns egenskaper när individernas propensity score skattas med  en  viktad  logistisk  regressionsmodell  gentemot  när  individernas  propensity score skattas med en logistisk regressionsmodell utan vikter. Viktad logistisk regressionsmodell innebär att en behandlings sanna prevalens i populationen  och  populationens subgrupper är  känd  och  inkluderas  i  modellen, vilket resulterar i att skattningar av propensity score kommer att vara väntevärdesriktiga. I den logistiska regressionmodellen utan vikter inkluderas inte den sanna prevalensen när propensity score ska skattas och skattningarna av propensity score kommer inte vara väntevärdesriktiga. Egenskaper som jämförs är bias, standardavvikelse och MSE. Resultatet av uppsatsen visade ingen minskning av MSE när prevalensen avbehandlingen i populationen inkluderades vid skattningen av observationernas propensity score. Estimatorn där behandlingens prevalens inte inkluderades vid skattningen av observationernas propensity score resulterade i lägre bias och MSE, men högre standardavvikelse. Båda estimatorernas bias gickmot noll när stickprovstorleken ökade.

Due to a phenomenon known as selection bias, the estimator of the average treatmen teffect (ATE) of a treatment variable on some outcome may be biased. Selection bias, caused by exclusion of possible units from the studied data, is a major obstacle to valid statistical and causal inferences. It is hard to detect in experimental or observational studies and is introduced when conditioning a sample on a common collider of the treatment and response variables. A certain type of selection bias known as M-Bias occurs when conditioning on a pretreatment variable that is part of a particular variable structure, the M structure. In this structure, the collider has no direct causal association with the treatment and outcome variables, but it is indirectly associated with both through ancestors. In this thesis, scenarios where potential M-bias arises were examined in a simulation study. The percentage of bias relative to the true ATE was estimated for each of the scenarios. A continuous collider variable was used and samples were conditioned to only include units with values on the collider variable above a certain cutoff value.T he cutoff value was varied to explore the relationship between the collider and theresulting bias. A variation of the M structure known as the butterfly structure was also studied in a similar fashion. The butterfly structure is known to result in confounding bias when not adjusting for said collider but selection bias when adjustment is done. The results show that selection bias is relatively small compared to bias originating from confounding in the butterfly structure. Increasing the cutoff level in this structure substantially decreases the overall bias of the ATE in almost all of the explored scenarios. The bias was smaller in the M structure than in the butterfly structure in close to all scenarios. For the M structure, the bias was generally smaller for higher cutoff values and insubstantial in some scenarios. This occurred because in most of the studied scenarios, a large proportion of the variance of the collider was explained by binary ancestors of said collider. When these ancestors are the primary causes of the collider, increasing the cutoff to a high enough value causes adjustment for the ancestors. Adjusting for these ancestors will in turn d-separate the treatment and the outcome which results in an unbiased estimator of the ATE. When conducting studies in pratice, the possibility of selection bias should be taken into consideration. Even though this type of bias is usually small even whe nthe causal effects between involved variables are strong, it can still be significant and an unbiased estimator cannot be taken for granted in the presence of sample selection.

Den longitudinella Betula-studien studerar relationen mellan minne och åldrande. Denna studie undersöker, med hjälp av givet data, om det finns skillnad mellan de individer som föll bort och de som återkom, samt vilka egenskaper som kan ha påverkat bortfallet. Datamaterialet är uppbyggt på ett stickprov av 176 deltagare från Betulas femte undersökningstillfälle, varav 70 individer var bortfall, de som ej deltog vid det sjätte undersökningstillfället, medan 106 individer återkom. Med hjälp av Little ́s MCAR-test framkom bevis för att kunna förkasta att data från det sjätte tillfället saknades slumpmässigt. Detta pekade på att bortfallet var påverkad av faktorer i antingen det givna eller icke-existerande datamaterialet. Sedan användes klassificeringsmetoder logistisk regression och random forest för att undersöka vilka faktorer, från det givna datamaterialet, som kan ha påverkat utfallet. Resultaten från den logistiska regressionsmodellen visade på att män hade större odds att falla bort från studien än kvinnor och att högre poäng på tester som undersöker episodiskt minne och bearbetningshastighet minskade oddset. Resultatet från analys med random forest pekade på att de som föll bort och de som återkom skiljde sig åt i variabeln volymen av grå substans i hippocampus samt i fyra kognitionstester. Två av testerna, som undersöker episodiskt minne och bearbetningshastighet, visade betydelse med båda modellerna. Testresultat från block design och ordflöde visade sig endast ha betydelse med random forest.