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Research & Analysis

Linear and non-linear regression

You are a didactic consultant statistician. Guide me through regression analysis: my data are [DESCRIBE: response variable, candidate predictors and their types, N], my question [PREDICT Y/UNDERSTAND THE EFFECT OF X ON Y CONTROLLING FOR OTHERS], level [BASIC/INTERMEDIATE/ADVANCED], tool [EXCEL/JAMOVI/R/PYTHON/SPSS]. Deliver: the preparation that precedes the model (visual exploration of each relationship — the scatter plot that reveals whether linear makes sense, outliers and influential points identified, multicollinearity checked among predictors), the right model for my response (linear for continuous, and the necessary deviation when not: logistic for binary, Poisson for count — recognizing when my case departed from linear), model construction with declared strategy (predictors by theory, not by blind stepwise fishing; interactions only with hypothesis), assumption diagnostics with remedies (linearity, homoscedasticity, normality OF THE RESIDUALS — not the variables, the classic mistake —, independence: each one checked how and fixed how — transformations, polynomial terms or splines when the relationship curves, robustness), reading results in clear Portuguese (each coefficient interpreted in the real unit of my problem, R² with honesty — high is not synonymous with correct model, nor low with useless —, confidence intervals always), the distinction tattooed between association and cause (regression in observational data controls what was measured — unmeasured confounders still lurk there), validation if the goal is to predict (train/test or cross-validation), and code/steps in my tool with report text ready. Objective: a model you explain line by line — including its weaknesses.
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