Hello, I'm Udita Bista

In Project 01 (Simple Linear Regression), I demonstrate Objective 1 by treating probability and inference as the backbone of every analytical decision, not just a final reporting step. The core of this objective is the understanding that statistical modeling is fundamentally about quantifying uncertainty - and this project shows that in practice. For the Auto dataset, I used p-values to formally test whether the relationship between horsepower and mpg was statistically distinguishable from chance, arriving at a p-value well below 0.05 and concluding the relationship is real. More importantly, I went beyond the point estimate by computing 95% confidence intervals for the mean response and 95% prediction intervals for individual observations, making explicit the difference between uncertainty about the average car and uncertainty about any specific car - a distinction that sits at the heart of inferential reasoning.

The Boston housing analysis extended this inferential framework to a train/test validation context, which connects probability directly to predictive modeling. I used the fitted model to generate predictions on held-out data and quantified uncertainty around those predictions through both interval estimates and performance metrics (RMSE, R²). The bias-variance trade-off comparison between linear and cubic models also demonstrates probabilistic thinking: a cubic model minimizes training error but inflates variance, meaning its predictions are less reliable in expectation on new data. Understanding that a model's behavior on training data is a biased estimate of its true generalization performance is itself a probabilistic insight - and one that I applied concretely by selecting the simpler model on principled grounds rather than just chasing a lower RSS.

Maximum likelihood estimation (MLE), which underpins linear regression through the assumption of normally distributed errors, also informed how I interpreted my diagnostic plots. The Q-Q plot is a direct visual check of the normality assumption that MLE depends on; the residual-vs-fitted plot checks homoscedasticity, which affects the validity of standard errors and therefore all downstream inference. By working through these diagnostics and explaining what each violation would mean for the reliability of my p-values and intervals, I demonstrated that inference is not a mechanical output but a conclusion that is only valid when the probabilistic assumptions behind the model are adequately met. This disciplined approach to assumption-checking is what makes the inferential claims in the report trustworthy rather than merely reported.

Objective 2 asks me to apply the appropriate generalized linear model for a specific data context, and across three projects I worked with three different GLM families that each demanded a different distributional assumption. In Project 02 (Carseats), I applied multiple linear regression with both a quantitative predictor (Price) and a qualitative predictor (ShelveLoc), along with their interaction. The inclusion of an interaction term meant the model produced three distinct regression lines - one per shelf location category - and interpreting those lines required understanding not just the math but what the conditional slopes actually mean: for Good shelf locations, each one-dollar increase in price reduces predicted sales by 0.063 units, versus only 0.050 for Bad locations. Choosing this model over a simpler additive one was itself a modeling decision grounded in the data, as my ggpairs exploration showed that shelf location visibly separated the data into distinct groups before I fit anything.

In Project 04 (Nonvoters), I applied multinomial logistic regression to a three-class outcome - always, sporadic, and rarely/never voters - from a set of demographic and party affiliation predictors. Selecting multinomial regression here was the appropriate choice because the outcome had more than two unordered categories, and binary logistic regression would have thrown away information. I wrote out both log-odds equations in full, converted those equations into odds-ratio statements (e.g., Democrats have 305.9% higher odds of being always vs rarely/never voters than the "Other" reference group), and compared model performance with and without party affiliation. In Project 06 (K-12 PFI), I applied Negative Binomial regression to a count outcome - times parents participated in school activities - after diagnosing severe overdispersion (variance-to-mean ratio = 12.2). Standard Poisson assumes variance equals the mean; when that assumption is violated, standard errors are underestimated and hypothesis tests become invalid. Switching to Negative Binomial and quantifying the AIC improvement of ~34,944 points demonstrated that choosing the right distributional family is not a formality — it is a substantive modeling decision with real consequences for the reliability of inference.

Across all three projects, what tied these choices together was the same underlying discipline: before selecting a model, I examined the data structure and the nature of the outcome, then matched the model family to those properties. That diagnostic-first mindset - rather than defaulting to the most familiar method - is what I take as the core of Objective 2, and it is a habit I will carry into every analysis I do going forward.

Objective 3 requires me to demonstrate model selection given a set of candidate models, and the two projects that best illustrate this are Project 03 (Auto backward elimination) and Project 05 (Diamonds best subset). In Project 03, I performed two sequential rounds of elimination on the Auto dataset: first, a manual backward elimination by p-value that removed mpg, cylinders, and year one at a time, tracking adjusted R² at each step; second, a VIF-based elimination that removed displacement due to severe collinearity with the remaining predictors. The final model - predicting acceleration from horsepower and weight - was arrived at through a documented, step-by-step process with a clear rationale at every stage. The most important lesson here was that eliminating a predictor because it is collinear, even if it is individually significant, is a legitimate and necessary modeling decision when the goal is producing stable, interpretable coefficient estimates rather than maximizing R².

In Project 05 (Diamonds), our group applied best subset selection across 25 candidate predictors using regsubsets(), then used a held-out validation set - not training-set criteria - to objectively choose the final model size. This three-way split (64% training, 16% validation, 20% test) meant that every model selection decision was made on data the final model had never seen. The validation set selected a 5-predictor polynomial model - table, poly(x, 2), and poly(z, 2) - and the held-out test R² of 0.997 confirmed that the selection procedure generalized well. An interesting finding was the sharp spike in validation MSE when model size jumped from 7 to 8 predictors, which I traced back to the instability introduced by adding a partially included categorical variable (cut) alongside already-collinear dimension predictors. That investigation taught me that model selection criteria are not monotone, and a larger model is not always a better one - a principle that applies far beyond this dataset.

What both projects share is a commitment to making model selection decisions with data the model has not already learned from. Whether through adjusted R², VIF thresholds, or validation-set MSE, the underlying principle is the same: a model's value is measured by how well it works on new data, not on the sample used to fit it. Applying this principle consistently is what turns model selection from a mechanical procedure into a form of genuine statistical reasoning.

Objective 4 asks me to express the results of statistical models to a general audience, and this is where I feel I grew the most over the course of the semester. My early analyses tended to report coefficients and metrics without translation - a slope of -0.05, an R² of 0.57 - and leave the interpretation to the reader. By Projects 04 and 06, I had developed a consistent practice of converting every model output into a plain-language statement before moving on. In Project 04 (Nonvoters), instead of reporting that the Democrat party indicator had a coefficient of 1.401 in the log-odds equation, I computed the exponentiated odds ratio and reported that Democrats have 305.9% higher odds of being always voters compared to rarely/never voters relative to the "Other" reference group. For the gender slope, I translated -0.192 log-odds into a 17.47% reduction in the odds of being an always voter - a number a policymaker or journalist could actually use. I also explained the confusion matrix in plain terms, naming the model's central-category bias and describing why sporadic was over-predicted structurally, not just as an observed error rate.

In Project 06 (K-12 PFI), the communication challenge was larger because we had multiple models and multiple outcome types running in parallel. For the Negative Binomial model, I reported that each additional school activity a parent participated in multiplied their expected participation count by 1.29 - framing the result multiplicatively because that is how Negative Binomial coefficients work on the original scale, and because a multiplication factor is more intuitive than a log-count change for a non-statistical audience. For the logistic regression, I used plain English to describe the magnitude and direction of every significant predictor: children without a disability have 65% lower odds of being a non-high-achiever; girls have 42% lower odds than boys; each step up in household income is associated with slightly higher odds of academic achievement. These are findings with real meaning for school administrators and policymakers, and communicating them honestly required thinking carefully about not just what to say but how to say it without overstating certainty or hiding limitations.

The skill I developed through this objective goes beyond writing. Learning to translate statistical output into accessible language also forced me to check whether I actually understood what I was reporting. If I could not explain a coefficient in words without jargon, it usually meant I had not fully internalized what the model was doing. In that sense, Objective 4 functioned as a diagnostic for all the other objectives - a way of catching gaps in understanding that numerical outputs alone would not surface.

Objective 5 requires me to use programming software to fit and assess statistical models, and the two projects that best showcase this proficiency are Projects 05 and 06. In Project 05 (Diamonds), I used regsubsets() from the leaps package for exhaustive best subset selection across 25 candidate predictors - a procedure that would be computationally impractical to do manually. I then built a validation-set loop to compute prediction error for every model size, identified the best size programmatically, refitted the final model using poly() for orthogonal polynomial encoding (rather than raw squared terms), and confirmed via vif() that collinearity was resolved. The full pipeline - data cleaning, three-way splitting with set.seed() for reproducibility, model selection, diagnostics, and held-out test evaluation - was written in R Markdown with code and narrative interwoven throughout, producing a document that is both a working analysis and a readable report. Working with 53,940 observations also required attention to code efficiency that smaller datasets do not demand.

In Project 06 (K-12 PFI), the technical scope was even broader. I worked with a real government survey dataset containing 75 variables and meaningful missing-value codes (negative integers as valid skips), which required careful recoding before any analysis could begin. The modeling workflow spanned four different model types within a single document: glm.nb() for Negative Binomial regression, logistic_reg() with the glm engine, multinom_reg() with the nnet engine (including repair_call() to fix tidymodels' internal call storage), and discrim_linear() / discrim_quad() with the MASS engine for LDA and QDA. Across all models, I used an 80/20 stratified train/test split, computed AIC comparisons and likelihood ratio tests for model selection, and evaluated final performance using metric_set(), conf_mat(), and roc_curve(). The upsampling for the multinomial model was implemented through a full tidymodels recipe using step_upsample() from themis - applied only to training data via prep() and bake() - ensuring that the test set remained in its natural distribution for an honest evaluation.

What these two projects demonstrate together is not just that I can run the functions, but that I understand when to use which tool and why. Choosing poly() over raw squared terms, stratifying the split by the outcome variable, repairing the model call before augmenting - each of these decisions required knowing something about how R and tidymodels work internally, not just what the surface-level syntax looks like. That depth of technical understanding is what I mean by proficiency, and it is the foundation on which all the other objectives in this portfolio ultimately rest.

Throughout STA 631, I made a point of attending every class and ensuring I genuinely understood the material being delivered rather than simply being present. When something was unclear, I asked questions in class and followed up with internet research on my own time to fill in any gaps. I found that taking this extra step - going beyond what was covered in the session - helped me build a more solid foundation before moving on to the next topic.

The assignments and projects were especially valuable in reinforcing that understanding. Each one gave me an opportunity to revisit concepts from class and apply them to real data, which revealed gaps in my comprehension that lectures alone had not surfaced. When I ran into confusion, I worked through it by discussing with classmates, and when I had a clearer grasp of something a peer was struggling with, I offered an explanation in return. That back-and-forth was one of the most effective parts of my learning process throughout the semester.

Two projects in this portfolio - Projects 05 and 06 - were completed in groups. Collaborating on those analyses pushed me to articulate methodological decisions clearly to teammates: why we removed zero-dimension diamonds, why we used a three-way split, why we switched from Poisson to Negative Binomial. Having to justify those choices to collaborators, not just to an instructor, held me to a higher standard of clarity that I carried back into my individual work as well.