In practice, when one has many candidate variables as explanatory variables in multiple regression, there is always the possibility that variables that are important determinants of the response variable might be omitted from the model, while unimportant variables might be included. Both types of errors are important, and in this dissertation it is attempted to quantify the probabilities of these errors. A simulation study is reported in this dissertation. Different numbers of variables, i.e. p= 4 to 20 are assumed, and different sample sizes, i.e. n=0.5p, p, 2p, 4p. For each p the underlying model assumes that roughly half of the independent variables are actually correlated with the dependant variable and the other half not. The noise is ε~ N(0, σ2, where σ2, is set fixed. The data was simulated 10000 times for each combination of n and p using known underlying models and ε randomly selected from of a normal distribution. For this investigation the full model and forward selection regression are compared. The mean squared error of the estimated coefficient β(p) is determined from the true β of each n and p set. A full discussion, as well as graphs, is presented. / Dissertation (MSc)--University of Pretoria, 2011. / Statistics / unrestricted

Across the world countries are currently striving to eliminate poverty, improve the quality of education, optimize well-being, among other areas of improvement. In an effort to help such improvements, a group called Young Lives ran a longitudinal study on youth in Ethiopia, India, Peru, and Vietnam that studied the many facets of poverty. The purpose of this study is to utilize the Young Lives dataset to determine how countries can more readily improve social-emotional skills by looking at important experiences in adolescents' lives. Specifically, this study examines what factors increase a child's ability to socialize with peers, which is shown to be linked to higher academic success as well as a fuller development into adulthood. In order to measure the ability to socialize with peers, Young Lives used the relationships with Peers Scale (RPS). I examined, through implementing structural equation modeling techniques, what factors significantly predict RPS scores, as well as which time point the factors are most predictive. I also inspected the psychometric properties of the RPS on the Young Lives' population and observed measurement invariance across time and country in order to ensure this scale is a valid measure. Steps to improve relationships with peers can be taken by encouraging higher intrinsic locus of control, providing equal educational opportunities, improving safety conditions, providing nutritional education, and eliminating competition for resources.

The recent observed growth in the diffusion of Special Purpose Acquisition Companies phenomena on the U.S stock market may be analyzed from a mathematical standpoint, where different approaches of the Bass Diffusion Model might be utilized. The Bass diffusion model originates from analysis of product diffusion, where only a few applications have been seen by financial scholars. The thesis takes a multi analytical approach to examine the phenomena, where multiple regression analysis and Bayesian statistics are used in the parameter estimation processes. Estimated parameter are applied in three different scenarios of expressing the Bass diffusion model in a discrete time state. By utilizing these different approaches that arise, the study shows that the diffusion of Special Purpose Acquisition Companies Initial Public Offerings in fact can be analyzed from a mathematical standpoint utilizing the Bass diffusion model. Some approaches and scenarios indicate better results in terms of fitting the diffusion, while purposing practical actualities towards the reader and market practitioners. The study further purposes potential modifications that might improve the results of fitting the phenomena

PURPOSE: The method for streamflow forecasting by using Fourier Series and Multiple Regression as a mathematical model have been suggested and proved with high accuracy for the streamflow forecasting on Logan River, Utah by Professor Cleve H. Milligan and Dr. Rex L. Hurst. In this thesis the method is extended to the forecasting for the Blacksmith Fork River, south of the Logan River. Because the climatological data are not available in the Blacksmith Fork watershed, this thesis also provides a technique for using the available data from adjacent watersheds. OBJECTIVES: 1. To forecast the streamflow on Blacksmith Fork River, Cache County, Utah by using Fourier Series and Multiple Regression as a mathematical model. 2. To test the consistency of the snow, temperature, precipitation, and streamflow data by statistical methods. 3. To test the significance of the variables considered in the mathematical model.

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京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18583号 / 工博第3944号 / 新制||工||1606(附属図書館) / 31483 / 京都大学大学院工学研究科建築学専攻 / (主査)教授 門内 輝行, 教授 髙田 光雄, 教授 神吉 紀世子 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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PM2.5 variability within the neighborhood scale has not been thoroughly studied for wood burning communities. High variability in near-field PM2.5 concentration may lead to harmful public exposure since monitoring does not occur on that scale. This study measures near-field PM2.5 variability by measuring black carbon (BC), a component of PM2.5, in a 1 km2 area located in Cambria, California. BC and meteorological data (when meteorological instruments were available) were measured over thirteen 12-hour intensive operation periods (IOPs) occurring over the winters of 2009 and 2010. Near-field BC variability was measured to understand the type of exposures found in communities where many homes are burning wood simultaneously within a small area. In addition, relationships between meteorological, geographical, and burning source characteristics and BC were observed as tools for understanding BC concentration. The computer air dispersion modeling programs, ISC-PRIME and ISCST3, were also evaluated for applicability to the near field. BC concentrations were measured using 1- to 2-minute resolution aethalometers and 12 hour resolution Personal Environmental Monitors (PEMs). On average, over all IOPs and sites, aethalometer and PEM BC averages were very similar, ranging between 200 and 250 ng/m3, or 4 and 5 µg/m3 for PM2.5, and standard deviations were often high. Averaging all BC measurements, aethalometer BC standard deviation values were 360 percent of the average BC concentration and PEM BC standard deviations were 120 percent the average BC concentration. The average standard deviation detected during each IOP was 190 percent of the average BC concentration for aethalometers and 79 percent of the average BC concentration for PEMs. The average standard deviation detected at each site was 220 percent of the average BC concentration for aethalometers and 76 percent of the average BC concentration for PEMs. The larger standard deviations measured by higher resolution aethalometers demonstrated that low resolution instruments, such as PEMs, are unable to detect high concentrations that may occur. In addition to examining BC variability, multiple linear regression analyses were conducted to determine the impact of meteorological variables and geographic and burning source characteristics on BC concentration and a weighted BC deviation function (BC standard deviation divided by average BC concentration). Time impacts, humidity, and wind speed, accounted for about 50 percent of variability in aethalometer average BC and BC deviation. However, because all model assumptions were not satisfied, improvements are needed. Regression models based on PEM BC found wind speed and direction to account for about 80 percent of average PEM BC variability and number of burning sources to account for about 30 percent of PEM BC deviation. Although PEM BC models accounted for a high percentage of BC variability, few data points were available for the PEM analyses and more IOPs are needed to determine their accuracy. When evaluating correlations between geographic and burning source characteristics and PEM BC concentrations, specific IOP and PEM sampling location explained almost 70 percent of variability in BC concentration, though model residuals suggested model bias. IOP likely explained variation in burning patterns and meteorology over each night while sampling location was likely a proxy for housing density, tree coverage, and/or elevation. Because all regression model assumptions could not be satisfied, the predictors were also observed graphically. Plotting BC concentration versus the number of burning sources suggested that number of burning sources may affect BC concentration in areas of low tree coverage and high housing density and in the case that the level of surrounding vegetation and structures are minimal. More data points will be needed to determine whether or not these relationships are significant. ISC-PRIME and ISCST3 modeling overall tended to under predict BC concentrations with average modeled-to-measured ratios averaging 0.25 and 0.15, for ISC-PRIME and ISCST3, respectively. Correction factors of 9.75 and 18.2 for ISC-PRIME and ISCST3, respectively, were determined to bring modeled BC concentrations closer to unity, but the range of ratios was still high. Both programs were unable to consistently capture BC variability in the area and more investigation will be needed to improve models. The results of the study indicate high BC variability exists on the near-field scale, but that the variability is not clearly explained by existing regression and air dispersion models. To prevent public exposure to harmful concentrations, more investigation will be needed to determine factors that largely influence pollutant variability on the neighborhood scale.

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