Inom fondförvaltning används kvantitativa metoder för att förutsäga hur företags räkenskaper kommer att förändras vid nästa kvartal jämfört med motsvarande kvartal året innan. Banken SEB använder i dag multipel linjär regression med förändring av intäkter som beroende variabel och förändring av valutakurser som oberoende variabler. Det är problematiskt av tre anledningar. Först och främst har valutor ofta stor multikolinjäritet, vilket ger instabila skattningar. För det andra det kan ett företags intäkter bero på ett urval av de valutor som används som data varför regression inte bör ske mot alla valutor. För det tredje är nyare data mer relevant för prediktioner. Dessa problem kan hanteras genom att använda regulariserings- och urvalsmetoder, mer specifikt elastic net och viktad regression. Vi utvärderar dessa metoder för en stor mängd företag genom att jämföra medelabsolutfelet mellan multipel linjär regression och regulariserad linjär regression med viktning. Utvärderingen visar att en sådan modell presterar bättre i 65,0 % av de företag som ingår i ett stort globalt aktieindex samt får ett medelabsolutfel på 14 procentenheter. Slutsatsen blir att elastic net och viktad regression adresserar problemen med den ursprungliga modellen och kan användas för bättre förutsägelser av intäkternas beroende av valutakurser. / Quantative methods are used in fund management to predict the change in companies' revenues at the next quarterly report compared to the corresponding quarter the year before. The Swedish bank SEB already uses multiple linear regression with change of revenue as the depedent variable and change of exchange rates as independent variables. This is problematic for three reasons. Firstly, currencies often exibit large multicolinearity, which yields volatile estimates. Secondly, a company's revenue can depend on a subset of the currencies included in the dataset. With the multicolinearity in mind, it is benifical to not regress against all the currencies. Thirdly, newer data is more relevant for the predictions. These issues can be handled by using regularisation and selection methods, more specifically elastic net and weighted regression. We evaluate these methods for a large number of companies by comparing the mean absolute error between multiple linear regression and regularised linear regression with weighting. The evaluation shows that such model performs better for 65.0% of the companies included in a large global share index with a mean absolute error of 14 percentage points. The conclusion is that elastic net and weighted regression address the problems with the original model and can be used for better predictions of how the revenues depend on exchange rates.

Public transport is essential for both residents and city planners because of its environmentally and economically beneficial characteristics. During the past decade climatechange, coupled with fuel and energy crises have attracted significant attention toward public transportation. Increasing the demand for public transport on the one hand and its complexity on the other hand have made the optimum network design quite challenging for city planners. The ridership is affected by numerous variables and features like space and time. These fluctuations, coupled with inherent uncertaintiesdue to different travel behaviors, make this procedure challenging. Any demand and supply mismatching can result in great user dissatisfaction and waste of energy on the horizon. During the past years, due to recent technologies in recording and storing data and advances in data analysis techniques, finding patterns, and predicting ridership based on historical data have improved significantly. This study aims to develop forecasting models by regressing boardings toward population, time of day, month, and station. Using the available boarding dataset for blue bus line number 4 in Stockholm, Sweden, seven different machine learning algorithms were assessed for prediction: Multiple Linear Regression, Decision Tree, Random Forest, Bayesian Ridge Regression, Neural Networks, Support Vector Machines, K-Nearest Neighbors. The models were trained and tested on the dataset from 2012 to 2019, before the start of the pandemic. The best model, KNN, with an average R-squared of 0.65 in 10-fold cross-validation was accepted as the best model. This model is then used to predict reduced ridership during the pandemic in 2020 and 2021. The results showed a reduction of 48.93% in 2020 and 82.24% in 2021 for the studied bus line.

I denna studie ska prisutvecklingen undersökas inom fastighetsbranschen från 2017 till 2020 genom att bygga upp multipel linjära regressionsmodeller. Fokusområdena omfattar Östermalm, Sundbyberg och Kista. Modeller framställs för respektive område separat, och bygger på data från Svensk Mäklarstatistik. Datamaterialet täcker respektive år mellan 2017 fram till 2020 för månaderna januari, april och september. För varje modell undersöks de grundläggande kriterierna inom regressionsanalys. Det används en stegvis metod för att konstruera en så optimal modell som möjligt. Därefter genomförs en gemensam regression som inkluderar samtliga datapunkter för samtliga områden, med område som indikatorvariabel, i syfte att undersöka om geografiska skillnader har en inverkan på bostadspriserna. Därav diskuteras modellernas trovärdighet baserat på de valda förklarande variablerna samt vilka variabler som har störst inverkan på priset. Resultatet visar att Boyta är mest signifikant för bostadspriser i Kista och Sundbyberg samt att Byggnadsår är mest signifikant för priser i Östermalm. Vidare har det konstaterats att det är möjligt att utveckla en regressionsmodell på ett godtagbart sätt, men det krävs vidare studier på en mer avancerad nivå för att få en mer realistisk bild på bostadsmarknaden. / In this thesis, the price development in the real estate industry from 2017 up to 2020 will be investigated by building multiple linear regression models. The focus areas include Östermalm, Sundbyberg and Kista. Models are prepared for each area separately, and are based on data from Svensk Mäklarstatistik. The data material covers the respective years between 2017 and 2020 for the months of January, April and September. For each model, the basic criteria in regression analysis are examined. A stepwise method is used to develop the most possible optimal model. A joint regression is then carried out that includes all data points för all areas, with area as a dummy variable, in order to investigate whether geographical differences have an impact on the real estate price. Hence, the credibility of the models is discussed based on the selected explanatory variables and which variables have the greatest impact on the housing prices. The result shows that Living area is most significant for real estate prices in Kista and Sundbyberg and that Build year is most significant for real estate prices in Östermalm. Furthermore, it has been established that it is possible to develop a regression model in an acceptable way, but further studies are required at a more advanced level to get a more realistic picture of the housing market.

This thesis is a case study in collaboration with SJ AB, a government owned railway companyin Sweden. The employees aboard the trains are an essential part of operating thetrains efficiently. Therefore, it is vital to forecast absences well in order to avoid havingto cancel train trips or having employees work over time. The current process SJ usesdivides the total amount of absences into 11 categories representing reasons for not beingpresent. This is done three months in advance, but the model is not based on mathematics.This study is going to examine how well the forecasts compare to reality in addition toinvestigating which variables are possible to estimate using regression analysis. Furthermore,the extent to which the staff on board the trains are affected will be investigatedin terms of having to work less overtime. The financial impact of an enhanced model willbe researched. “Free” days, Vacation and Sickness all have significant regressors and canpotentially be forecast using regression analysis. Future work includes finding more potentialregressor variables that could be significant for more response variables in addition tousing the results of this thesis in an actual estimation model for the total absence. / Denna avhandling ärr en fallstudie i samarbete med SJ AB, ett statligt ägt järnvägsföretagi Sverige. Anställda ombord på tågen utgör en väsentlig del av att driva tågverksamheteneffektivt. Det är därför viktigt att kunna prognostisera frånvaro väl för att undvika attställa in rutter eller tvinga de anställda ombord tåget att arbeta övertid. Den nuvarandeprocessen som SJ använder delar upp den totala mängden frånvaro i 11 kategorier somrepresenterar orsaker till att inte vara närvarande. Detta görs tre månader i förväg, menmodellen är inte baserad på matematik i dagsläget. Denna studie kommer att undersökahur väl prognoserna stämmer överens med verkligheten, samt undersöka vilka variabler somör möjliga att uppskatta med hjälp av regressionsanalys. Dessutom kommer omfattningenav hur personalen ombord på tågen påverkas att undersökas. Den ekonomiska påverkanav en förbättrad modell kommer att analyseras. Lediga dagar, semester och sjukfrånvarohar alla signifikanta beskrivande variabler och kan potentiellt prognostiseras med hjälp avregressionsanalys. Framtida arbete innefattar att hitta fler potentiella beskrivande variablersom kan vara signifikanta för fler beroende variabler, samt att använda resultatenfrån denna avhandling i en faktisk prognosmodell för total frånvaro.

Arbetet syftade till att finna en passande modell för Moraberg AB:s beställningsrutiner för två färskvaror av anledning att optimera lagernivåer och minska matsvinn. Då efterfrågan hos Moraberg AB var okänd togs en modell fram för att prediktera och undersöka ifall det fanns ett linjärt samband mellan ett par parametrar och efterfrågan. Parametrarna som undersöktes var veckodag, temperatur, nederbörd och antal smittade personer i Covid-­19. Modellen baserades på historisk försäljningsdata för åren 2018– 2020. Två efterfrågemodeller togs fram, den första modellen innehöll alla nämnda parametrar förutom antal smittade personer i Covid­-19 och den andra modellen innehöll alla parametrar. Resultatet visade att temperatur, nederbörd och antal smittade personer i Covid­-19 har ett svagt beroende med efterfrågan hos företaget men parametern veckodag visade ett högt beroende med efterfrågan. Analys av modellerna visade att det inte existerade multikollinearitet samt att de inte bröt de fem antagandena om regression. Vidare visade resultatet att modell 2 presterade bättre än modell 1. Lageroptimeringsmodellen som var lämpligast för Moraberg AB, med avseende på de resurser och begräsningar som fanns inom ramen av detta arbete, var den deterministiska periodiska inspektions modellen som kan lösas med dynamisk programmering. Ett numeriskt exempel genomfördes på den valda lageroptimeringsmodellen med hjälp av modell 2. Det numeriska exemplet baserades på prognoser från vecka 17 år 2021. / This thesis aimed to find a suitable inventory model for Moraberg AB’s ordering routines to optimize inventory levels and reduce food waste for two perishable products. As the demand at Moraberg AB was unknown, a regression model was developed to predict and investigate whether there was a linear relationship between a few parameters and the demand. The parameters examined were weekday, temperature, precipitation, and number of infected people in Covid­19. The model was based on historical sales data for the years 2018–2020. Two demand models were developed, the first model contained all the mentioned parameters except the number of people infected in Covid-­19 and the second model contained all parameters.  The results showed that temperature, precipitation, and number of people infected in Covid­-19 have a weak dependence with the demand, however the parameter weekday showed a dependence with the demand. Analysis of the two models did not show any signs of multicollinearity and they did not violate the five assumptions regarding regression. Furthermore, the results showed that model 2 performed better than model 1.  The inventory model that was most suitable for Moraberg AB, regarding the resources and limitations that existed within the framework of this thesis, was the deterministic periodic ­review model that could be solved by dynamic programming. A numerical example was solved using the suitable inventory model and with the second demand model. The numerical example was based on forecasts from week 17 year 2021.

This is a statistical analysis where various factors related to the Sustainable Development Goals (SDGs) have been used to explain life expectancy. The dataset contained information on how countries perform in different aspects over several years. The factors used have been considered to be well-linked to one or more of the SDGs by studying how the United Nations (UN) and Globalis have categorized them under different goals. After the dataset was investigated and measures were implemented, a multiple regression analysis was performed. The analysis showed which factors had statistically significant effects on life expectancy for the observations that were used. From this information, the final linear regression model could be obtained. Then it was discussed whether important information was omitted from the final model and another regression analysis was performed. This time, the dataset was divided into smaller subgroups where one group contained all observations where life expectancy was 75 years or more and the other data set contained all observations where life expectancy was 56 years or less. From these datasets, it was analyzed whether significant factors change depending on the associated life expectancy, which was proved to be the case. The conclusion that was drawn was therefore that the final model is a weighting of observations with different life expectancy, but the differences between observations with different life expectancies are omitted. / Det här är en statistisk analys där olika faktorer med koppling till de Globala Hållbarhetsmålen har används för att förklara den förväntade livslängden. Datasetet som användes innehöll information om hur länder presterar i olika avseenden under flera olika år. De faktorer som används har ansetts ha god koppling till något av de globala hållbarhetsmålen genom att studera hur FN samt Globalis har kategoriserat olika index under de respektive målen. Efter att datasetet undersökts och eventuella åtgärder genomförts så gjordes en multipel linjär regressionsanalys. Analysen visade vilka faktorer som hade signifikant påverkan på förväntad livslängd hos de observationer som använts. Ur denna information kunde den slutgiltiga linjära regressionsmodellen tas fram. Sedan skedde ett resonemang kring validiteten av denna modell och huruvida viktigt information utelämnas i den slutgiltiga modellen. Då genomfördes ytterligare en regressionsanalys, men denna gång hade datasetet delats upp i mindre grupper. En grupp innehöll alla observationer då den förväntade livslängden var 75 år eller mer, och den andra gruppen innehöll alla observationer då förväntad livslängd var 56 år eller mindre. Med hjälp av dessa dataset utreddes huruvida olika faktorer är olika viktiga vid olika förväntade livslängder, vilket var fallet. Slutsatsen som drogs var därför att den slutgiltiga modellen som togs fram var en sammanvägning av alla observationer med olika förväntade livslängder, men där skillnaderna mellan länder utelämnades.

An artificial neural network (ANN) is used to model nonlinear, large deformation plastic behavior of a material. This ANN model establishes a relationship between flow stress and dislocation structure content. The density of geometrically necessary dislocations (GNDs) was calculated based on analysis of local lattice curvature evolution. The model includes essential statistical measures extracted from the distributions of dislocation microstructures, including substructure cell size, wall thickness, and GND density as the input variables to the ANN model. The model was able to successfully predict the flow stress of aluminum alloy 6022 as a function of its dislocation structure content. Furthermore, a sensitivity analysis was performed to identify the significance of individual dislocation parameters on the flow stress. The results show that an ANN model can be used to calibrate and predict inelastic material properties that are often cumbersome to model with rigorous dislocation-based plasticity models.

Detta projekt undersöker coronapandemins påverkan på bostadsrätter i Stockholms kommun genom två multipel linjär regressionsanalyser med avseende på kvantitativa faktorer som försäljningspris, våningsplan, area, byggnadsår, månadsavgift och tillgång till hiss. Målet med projektet är att analysera om en förändring av preferenser har skett på transaktionsnivå för bostadsmarknaden i Stockholm kommun. För att möjliggöra analysen jämförs varje beta-koefficient från två olika dataset, en innan coronapandemin och en efter coronapandemin. Resultaten från multipel linjär regressionerna i denna undersökning visar för det första att hushållen i Stockholm värderar större area högre och för det andra att värdet av tillgång till hiss har haft en signifikant ökning efter coronapandemin. Där det första resultatet påvisar en fortsatt trend på ökad behov av arbetsrum till följd av distansarbete även efter coronapandemin. Däremot har betydelse av våningsplan, byggnadsår och månadsavgift minskat. Anledningen till minskningen påstås snarare vara en effekt av att andra variabler har blivit mer betydelsefulla. / This project examines the impact of the COVID-19 pandemic on condominiums in the Stockholm region by using two multiple linear regression analyses with respect to quantitative factors as sell price, year of construction, floor, area, monthly fee and access to elevator. The goal of this project is to analyze if a change of preferences have taken place at the transaction level for the real estate market in the Stockholm region. In order to enable the analysis, every beta-coefficient is compared from two different datasets, one before the pandemic and one after. The results of the multiple linear regressions shows firstly that the households in Stockholm value higher on larger areas and secondly that the value of the access to elevators after the pandemic has increased significantly. Whereas the first result proves a continuing trend with increasing demand for workrooms due to remote work even after COVID-19 pandemic. However, the impact of floor, year of construction and monthly fee has decreased. The reason behind the decrease is interpreted rather as an effect of that other variables have been more meaningful instead.

Return on Capital Employed (ROCE) is a popular financial instrument and communication tool for the appraisal of companies. Often, companies management and other practitioners use untested rules and behavioural approach when investigating the key determinants of ROCE, instead of the scientific statistical paradigm. The aim of this dissertation was to identify and quantify key determinants of ROCE of individual companies listed on the Johannesburg Stock Exchange (JSE), by comparing classical multiple linear regression, principal components regression, generalized least squares regression, and robust maximum likelihood regression approaches in order to improve companies decision making. Performance indicators used to arrive at the best approach were coefficient of determination ( ), adjusted ( , and Mean Square Residual (MSE). Since the ROCE variable had positive and negative values two separate analyses were done. The classical multiple linear regression models were constructed using stepwise directed search for dependent variable log ROCE for the two data sets. Assumptions were satisfied and problem of multicollinearity was addressed. For the positive ROCE data set, the classical multiple linear regression model had a of 0.928, an of 0.927, a MSE of 0.013, and the lead key determinant was Return on Equity (ROE),with positive elasticity, followed by Debt to Equity (D/E) and Capital Employed (CE), both with negative elasticities. The model showed good validation performance. For the negative ROCE data set, the classical multiple linear regression model had a of 0.666, an of 0.652, a MSE of 0.149, and the lead key determinant was Assets per Capital Employed (APCE) with positive effect, followed by Return on Assets (ROA) and Market Capitalization (MC), both with negative effects. The model showed poor validation performance. The results indicated more and less precision than those found by previous studies. This suggested that the key determinants are also important sources of variability in ROCE of individual companies that management need to work with. To handle the problem of multicollinearity in the data, principal components were selected using Kaiser-Guttman criterion. The principal components regression model was constructed using dependent variable log ROCE for the two data sets. Assumptions were satisfied. For the positive ROCE data set, the principal components regression model had a of 0.929, an of 0.929, a MSE of 0.069, and the lead key determinant was PC4 (log ROA, log ROE, log Operating Profit Margin (OPM)) and followed by PC2 (log Earnings Yield (EY), log Price to Earnings (P/E)), both with positive effects. The model resulted in a satisfactory validation performance. For the negative ROCE data set, the principal components regression model had a of 0.544, an of 0.532, a MSE of 0.167, and the lead key determinant was PC3 (ROA, EY, APCE) and followed by PC1 (MC, CE), both with negative effects. The model indicated an accurate validation performance. The results showed that the use of principal components as independent variables did not improve classical multiple linear regression model prediction in our data. This implied that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Generalized least square regression was used to assess heteroscedasticity and dependences in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the weighted generalized least squares regression model had a of 0.920, an of 0.919, a MSE of 0.044, and the lead key determinant was ROE with positive effect, followed by D/E with negative effect, Dividend Yield (DY) with positive effect and lastly CE with negative effect. The model indicated an accurate validation performance. For the negative ROCE data set, the weighted generalized least squares regression model had a of 0.559, an of 0.548, a MSE of 57.125, and the lead key determinant was APCE and followed by ROA, both with positive effects.The model showed a weak validation performance. The results suggested that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Robust maximum likelihood regression was employed to handle the problem of contamination in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the robust maximum likelihood regression model had a of 0.998, an of 0.997, a MSE of 6.739, and the lead key determinant was ROE with positive effect, followed by DY and lastly D/E, both with negative effects. The model showed a strong validation performance. For the negative ROCE data set, the robust maximum likelihood regression model had a of 0.990, an of 0.984, a MSE of 98.883, and the lead key determinant was APCE with positive effect and followed by ROA with negative effect. The model also showed a strong validation performance. The results reflected that the key determinants are major sources of variability in ROCE of individual companies that management need to work with. Overall, the findings showed that the use of robust maximum likelihood regression provided more precise results compared to those obtained using the three competing approaches, because it is more consistent, sufficient and efficient; has a higher breakdown point and no conditions. Companies management can establish and control proper marketing strategies using the key determinants, and results of these strategies can see an improvement in ROCE. / Mathematical Sciences / M. Sc. (Statistics)

Return on Capital Employed (ROCE) is a popular financial instrument and communication tool for the appraisal of companies. Often, companies management and other practitioners use untested rules and behavioural approach when investigating the key determinants of ROCE, instead of the scientific statistical paradigm. The aim of this dissertation was to identify and quantify key determinants of ROCE of individual companies listed on the Johannesburg Stock Exchange (JSE), by comparing classical multiple linear regression, principal components regression, generalized least squares regression, and robust maximum likelihood regression approaches in order to improve companies decision making. Performance indicators used to arrive at the best approach were coefficient of determination ( ), adjusted ( , and Mean Square Residual (MSE). Since the ROCE variable had positive and negative values two separate analyses were done. The classical multiple linear regression models were constructed using stepwise directed search for dependent variable log ROCE for the two data sets. Assumptions were satisfied and problem of multicollinearity was addressed. For the positive ROCE data set, the classical multiple linear regression model had a of 0.928, an of 0.927, a MSE of 0.013, and the lead key determinant was Return on Equity (ROE),with positive elasticity, followed by Debt to Equity (D/E) and Capital Employed (CE), both with negative elasticities. The model showed good validation performance. For the negative ROCE data set, the classical multiple linear regression model had a of 0.666, an of 0.652, a MSE of 0.149, and the lead key determinant was Assets per Capital Employed (APCE) with positive effect, followed by Return on Assets (ROA) and Market Capitalization (MC), both with negative effects. The model showed poor validation performance. The results indicated more and less precision than those found by previous studies. This suggested that the key determinants are also important sources of variability in ROCE of individual companies that management need to work with. To handle the problem of multicollinearity in the data, principal components were selected using Kaiser-Guttman criterion. The principal components regression model was constructed using dependent variable log ROCE for the two data sets. Assumptions were satisfied. For the positive ROCE data set, the principal components regression model had a of 0.929, an of 0.929, a MSE of 0.069, and the lead key determinant was PC4 (log ROA, log ROE, log Operating Profit Margin (OPM)) and followed by PC2 (log Earnings Yield (EY), log Price to Earnings (P/E)), both with positive effects. The model resulted in a satisfactory validation performance. For the negative ROCE data set, the principal components regression model had a of 0.544, an of 0.532, a MSE of 0.167, and the lead key determinant was PC3 (ROA, EY, APCE) and followed by PC1 (MC, CE), both with negative effects. The model indicated an accurate validation performance. The results showed that the use of principal components as independent variables did not improve classical multiple linear regression model prediction in our data. This implied that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Generalized least square regression was used to assess heteroscedasticity and dependences in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the weighted generalized least squares regression model had a of 0.920, an of 0.919, a MSE of 0.044, and the lead key determinant was ROE with positive effect, followed by D/E with negative effect, Dividend Yield (DY) with positive effect and lastly CE with negative effect. The model indicated an accurate validation performance. For the negative ROCE data set, the weighted generalized least squares regression model had a of 0.559, an of 0.548, a MSE of 57.125, and the lead key determinant was APCE and followed by ROA, both with positive effects.The model showed a weak validation performance. The results suggested that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Robust maximum likelihood regression was employed to handle the problem of contamination in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the robust maximum likelihood regression model had a of 0.998, an of 0.997, a MSE of 6.739, and the lead key determinant was ROE with positive effect, followed by DY and lastly D/E, both with negative effects. The model showed a strong validation performance. For the negative ROCE data set, the robust maximum likelihood regression model had a of 0.990, an of 0.984, a MSE of 98.883, and the lead key determinant was APCE with positive effect and followed by ROA with negative effect. The model also showed a strong validation performance. The results reflected that the key determinants are major sources of variability in ROCE of individual companies that management need to work with. Overall, the findings showed that the use of robust maximum likelihood regression provided more precise results compared to those obtained using the three competing approaches, because it is more consistent, sufficient and efficient; has a higher breakdown point and no conditions. Companies management can establish and control proper marketing strategies using the key determinants, and results of these strategies can see an improvement in ROCE. / Mathematical Sciences / M. Sc. (Statistics)