Statistical Concepts Explained and Applied in R

Install R and RStudio on Windows, compare the classic R console with the desktop RStudio IDE, and explore creating variables, loading packages, plotting, and basic data analyses.

Explore the basics of linear and simple linear regression, linking y to x and using models of linear, quadratic, exponential, or logarithmic forms, minimizing the sum of squares for prediction.

Examine scatter plots of X and Y to reveal linear and non-linear relationships, and apply a 30-observation rule to predict profits from advertising budgets using regression in R.

Learn to perform linear regression in R through a guided workflow, from loading data and preparing a data frame to creating a scatterplot of advertising budget versus profit.

Explore linear relationships with scatterplots and simple regression, linking advertising spend to profit through intercept and slope, and examine true vs estimated models and residuals.

Explore how the line of best fit minimizes the sum of squared deviations to form the least squares regression line, and analyze residuals, SSE, and MSE in linear regression.

Learn to perform linear regression in R using lm, naming the model, and interpret the linear model summary to analyze how advertising drives profit.

Explore regression results from a linear model in R, interpreting the intercept and slope, the advertising and profit relationship, and the model’s significance and reliability within data bounds.

Learn to generate and interpret predictions from a linear regression in R, create prediction plots with intervals, and forecast future profits under different advertising budgets.

Assess regression validity by examining residual plots for normality, constant variance, and independence of errors. Use transformations or alternative estimators when needed, and perform the Anderson-Darling test to confirm validity.

Examine regression diagnostics with residuals, normal probability plots, and Cook's distance. Use Anderson-Darling (p = 0.55) to confirm normality and guide transformations or outlier handling.

Explore multiple linear regression in R, using several predictors to explain a linear response, estimate coefficients, interpret one-unit changes holding others fixed, and assess normality, homoscedasticity, and independence.

Import and prepare the dataset in R by reading the file, attaching variables, and creating a data frame named D for 32 observations of six variables for a multiple linear regression.

Explore the correlation matrix before multiple linear regression, using a dummy location and two-digit rounding, and note advertising and new clients as significant predictors with an adjusted r-squared of 0.9217.

Compare model two with fewer variables using multiple linear regression and anova to assess significance, adjusted r-squared, and the impact of advertising and new clients on profit.

Explore how advertising and new referred clients positively affect profit in simple and multiple linear regression, and compare restricted versus control models using nested f tests and analysis of variance.

We explore interaction terms to better capture effects and use backward elimination to refine the model, then validate with anova and tests for heteroscedasticity and normality.

Explore how analysis of variance partitions model variance among advertising, offers, and location, interpret interactions, and use 80-20 training-test splits to build and compare regression predictions for management decisions.

Explore non-linear regression, heteroscedasticity effects on least squares, and when robust standard errors improve estimates. Learn generalized linear models with Bernoulli and binomial distributions and appropriate link functions.

Explore logistic regression for binary outcomes using the logit link, modeling probability with age-based investments, fitting in R, visualizing results, and comparing with linear regression.

Compare odds, odds ratios, and probability in logistic regression using log and exponential transformations of coefficients. Apply generalized linear models to discrete count data and interpret model scales.

Explore fitting logistic and related binomial models in R, comparing odds and risk ratios with confidence intervals, examining convergence, and using display, plotting, and Wald tests for model robustness.

Apply differential calculus to locate profit maxima and cost minima using first and second derivatives, and assess breakeven points and average cost in production.

This lecture shows a one unknown input differential calculus example to maximize profit from avocados and sweet apples within a $150 budget, accounting for transaction fees.

Learn how to apply one unknown input differential calculus in R to maximize profit by optimizing fruit quantities under a budget, using data frames, numeric conversion, and for loops.

Analyze differential calculus with two unknown outputs to reinvest daily cash flow from portfolio shares and referrals, and perform a six-month optimization of renewal periods.

Learn to load and transform data in R, automate monthly datasets with glue, and apply two unknown inputs differential calculus to optimize six-month renewal cash flow.