< Fernando Ramos >

Statistics 110 Sequence: Applied Statistics


$$ Y_{i} = \beta_{0} + \beta_{1}X_{i} + \epsilon_{i} \ ; \epsilon_{i} \sim N(0,\sigma_{\epsilon}^2) \ ; \sigma_{i}^2 = \sigma_{j}^2 \ \forall \ i \neq j $$ $95\% \ PI \Rightarrow \hat{Y_{h}} \pm t_{(\frac{\alpha}{2},\ n-2)} \sqrt{\hat{\sigma^{2}}\bigg(1 + \frac{1}{N} + \frac{X_{h}-\overline{X}}{\sum_{i=1}^{N}(X_{i}-\overline{X})^{2}}\bigg)}; \hat{\sigma^{2}} = \frac{\sum_{i=1}^{N}(Y_{i}-\beta_{0}-\beta_{1}X_{i})^{2}}{n-2} $

Stats 110

In this class we were introduced to statistical methods for analyzing data from experiments and surveys using the statistical computing language known as R. These methods included two-sample procedures, analysis of variance (ANOVA), simple and multiple linear regression. This class ultimately enhanced my data analysis skills and understanding of statistics. More time was spent on regression and its applications. The topics in regression that we studied were confidence intervals of parameters; F-statistic and t-statistic; null vs reduced model comparisons; diagnostic plots to detect violation of assumptions (linearity, constant variance, normality of residuals, independence of the data); interaction terms and polynomial terms; partitioning of variability (sums of squares); and prediction intervals. Emphasis was mostly on applications and understanding, not too much on theory. However, supplemental files and resources were provided to delve deeper into theoretical underpinnings of the models such as maximum likelihood estimation, ordinary least squares, and departures from distributional assumptions.

Selected Lectures & Other Files

Stats 111

Introduction to statistical methods for analyzing data from surveys or experiments. Emphasizes application and understanding of methods for categorical data including contingency tables, logistic and Poisson regression, loglinear models.

Stats 112

Introduction to statistical methods for analyzing longitudinal data from experiments and cohort studies. Topics covered include survival methods for censored time-to-event data, linear mixed models, non-linear mixed effects models, and generalized estimating equations.

Statistics 120 Sequence: Mathematical Statistics


$$\gamma (x;\alpha , \beta) = \frac{\beta^{\alpha}}{\Gamma(\alpha)}x^{\alpha - 1}e^{-\beta x}; x \in (0,\infty)\ ; \alpha , \beta >0\ ; \Gamma(\alpha) = \int_{0}^{\infty}x^{\alpha - 1}e^{-x}dx$$ $MLE \Rightarrow L(\beta, \sigma^{2}) = \prod_{i=1}^{N}\frac{1}{\sigma \sqrt{2\pi}} exp\{{\frac{-(Y_{i}-\beta_{0}-\beta_{1}X_{i})^{2}}{2\sigma^{2}}}\}; \hat{\beta_{0}} = \overline{Y} -\hat{\beta_{1}}\overline{X}\ ; \hat{\beta_{1}} = \frac{\sum_{i=1}^{N}(Y_{i} - \overline{Y})(X_{i} - \overline{X})}{\sum_{i=1}^{N}(X_{i} - \overline{X})^{2}}$

Stats 120A

Introduction to basic principles of probability and statistical inference. Axiomatic definition of probability, random variables, probability distributions, expectation.

Stats 120B

Introduction to basic principles of probability and statistical inference. Point estimation, interval estimating, and testing hypotheses, Bayesian approaches to inference.

Stats 120C

Introduction to basic principles of probability and statistical inference. Linear regression, analysis or variance, model checking.

Economics 122A & 122B: Applied Econometrics


$SST = \ SSR + \ SSE \Rightarrow \sum_{i=1}^{N}({Y_{i}}- \overline{Y})^{2} = \sum_{i=1}^{N}(\hat{Y_{i}}- \overline{Y})^{2} + \sum_{i=1}^{N}({Y_{i}}- \hat{{Y_{i}}})^{2}$

Econ 122A

In this class, we learned basic econometric theory and developed quantitative skills for elementary data analysis. We were primarily introduced to the econometric analysis of linear regression and its underlying assumptions, particularly those of normality and indepence of observations. Through a few problem sets, we gained practical experience by applying the econometric theory to actual economic data and performing inference using the models.

Econ 122B

Introduction to econometrics emphasizing practical applications in microeconomics and macroeconomics.

Economics 125: Business Forecasting


$$Y_{t} = \delta + \theta_{1}Y_{t-1} + \delta_{0}X_{t} + \delta_{1}X_{t-1} + V_{t}\rightarrow ARDL(1,1)$$

In this class, we learned how to produce forecasts of the behavior of economic (and other) variables. We reviewed the theory of linear regression with one regressor and multiple regressors. We also focused on regression with time-series data. Topics we covered in time series regression were unit root and cointegration tests (i.e Dickey-Fuller Test for stationarity); first and second order differencing; variable forecasts and prediction intervals; autoregressive distributed lag models and how to transform them into infinite distributed lag models; and serial correlation tests (i.e Lagrange Multiplier Test).

Selected Lectures & Other Files