Statistical inference, regression and model assumptions
Establish the population and design
Descriptive summaries characterize the supplied data; inferential claims require a relevant sampling or experiment model. A large sample can still be biased. Mean, median, spread, quantiles and visual distributions answer different questions. An outlier may be an error or a genuine important observation, so deletion needs justification. Independence, repeated measurements, missingness and selection affect which conclusions are supported.
Interpret uncertainty correctly
A frequentist confidence interval describes a procedure’s long-run coverage under its assumptions, not a posterior probability assigned to the fixed unknown parameter after the interval is observed. A p-value is a probability of results at least as extreme under the specified null model; it is not the probability that the null is true or a measure of practical importance. Statistical significance, effect size, uncertainty and decision costs should be considered together. Multiple comparisons and repeated tuning can change the evidential meaning of a promising result.
Understand regression targets
Linear regression models a conditional relationship under stated form and error assumptions. A fitted coefficient is conditional on the included variables and model, not automatically a causal effect. Residual diagnostics can reveal problems, and extrapolation beyond supported data is risky. Logistic regression models a binary outcome through a link such as log-odds; its raw linear score is not itself a probability. Multicollinearity can affect coefficient stability even when prediction remains useful.
Evaluate beyond the training fit
Separate training, model-selection validation and an appropriately held-out final evaluation. Fit preprocessing within the relevant training folds to avoid leakage. A low training error, large correlation or high accuracy does not establish fair deployment or good performance for rare costly outcomes. Choose precision, recall, calibration, error magnitude or other metrics for the actual task. Resampling must respect related records or time structure where needed. Predictive models require monitoring as conditions change. These exercises use supplied models and written reasoning, not real clinical, financial or legal decisions. The related statistics and machine-learning foundations are editorial preparation, not a claim of complete Google curriculum coverage or a guarantee of a model’s future performance.