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data-subkey="sec2sub3"><a href="/Statistical-Power-Analysis-in-R.html"><span class="progress-dot"></span>Power Analysis</a></li><li data-subkey="sec2sub3"><a href="/Effect-Size-in-R.html"><span class="progress-dot"></span>Effect Size</a></li><li data-subkey="sec2sub3"><a href="/t-Tests-in-R.html"><span class="progress-dot"></span>t-Tests</a></li><li data-subkey="sec2sub3"><a href="/Proportion-Tests-in-R.html"><span class="progress-dot"></span>Proportion Tests</a></li><li data-subkey="sec2sub3"><a href="/Normality-and-Variance-Tests-in-R.html"><span class="progress-dot"></span>Normality &amp; Variance Tests</a></li><li data-subkey="sec2sub3"><a href="/Chi-Square-Tests-in-R.html"><span class="progress-dot"></span>Chi-Square Tests</a></li><li data-subkey="sec2sub3"><a href="/Wilcoxon-Mann-Whitney-and-Kruskal-Wallis-in-R.html"><span class="progress-dot"></span>Wilcoxon, Mann-Whitney &amp; Kruskal-Wallis</a></li><li data-subkey="sec2sub3"><a href="/Multiple-Comparisons-in-R.html"><span class="progress-dot"></span>Multiple Testing Correction</a></li><li data-subkey="sec2sub3" class="is-quiz"><a href="/Hypothesis-Testing-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub4" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Regression</li><li data-subkey="sec2sub4"><a href="/Linear-Regression.html"><span class="progress-dot"></span>Linear Regression</a></li><li data-subkey="sec2sub4"><a href="/Logistic-Regression-With-R.html"><span class="progress-dot"></span>Logistic Regression</a></li><li data-subkey="sec2sub4"><a href="/Variable-Selection-and-Importance-With-R.html"><span class="progress-dot"></span>Feature Selection</a></li><li data-subkey="sec2sub4"><a href="/Model-Selection-in-R.html"><span class="progress-dot"></span>Model Selection</a></li><li data-subkey="sec2sub4"><a href="/Missing-Value-Treatment-With-R.html"><span class="progress-dot"></span>Missing Value Treatment</a></li><li data-subkey="sec2sub4"><a href="/Outlier-Treatment-With-R.html"><span class="progress-dot"></span>Outlier Analysis</a></li><li data-subkey="sec2sub4"><a href="/adv-regression-models.html"><span class="progress-dot"></span>Advanced Regression Models</a></li><li data-subkey="sec2sub4" class="is-quiz"><a href="/Linear-Regression-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub5" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Reporting</li><li data-subkey="sec2sub5"><a href="/Statistical-Consulting-in-R.html"><span 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class="progress-dot"></span>Interaction Effects</a></li><li data-subkey="sec2sub5"><a href="/Regression-Diagnostics-in-R.html"><span class="progress-dot"></span>Regression Diagnostics</a></li><li data-subkey="sec2sub5"><a href="/Logistic-Regression-in-R.html"><span class="progress-dot"></span>Logistic Regression (glm + ROC)</a></li><li data-subkey="sec2sub5"><a href="/Variable-Selection-in-R.html"><span class="progress-dot"></span>Variable Selection</a></li><li data-subkey="sec2sub5"><a href="/Poisson-Regression-in-R.html"><span class="progress-dot"></span>Poisson Regression</a></li><li data-subkey="sec2sub5"><a href="/Ridge-and-Lasso-Regression-in-R.html"><span class="progress-dot"></span>Ridge &amp; Lasso Regression</a></li><li data-subkey="sec2sub5"><a href="/Polynomial-and-Spline-Regression-in-R.html"><span class="progress-dot"></span>Polynomial &amp; Splines</a></li><li data-subkey="sec2sub5"><a href="/Regression-Tables-in-R.html"><span class="progress-dot"></span>Regression Tables (3 packages)</a></li><li data-subkey="sec2sub5"><a href="/One-Way-ANOVA-in-R.html"><span class="progress-dot"></span>One-Way ANOVA</a></li><li data-subkey="sec2sub5"><a href="/Post-Hoc-Tests-After-ANOVA.html"><span class="progress-dot"></span>Post-Hoc Tests After ANOVA</a></li><li data-subkey="sec2sub5"><a href="/Two-Way-ANOVA-in-R.html"><span class="progress-dot"></span>Two-Way ANOVA</a></li><li data-subkey="sec2sub5"><a href="/Repeated-Measures-ANOVA-in-R.html"><span class="progress-dot"></span>Repeated Measures ANOVA</a></li><li data-subkey="sec2sub5"><a href="/ANCOVA-in-R.html"><span class="progress-dot"></span>ANCOVA</a></li><li data-subkey="sec2sub5"><a href="/Experimental-Design-Principles-in-R.html"><span class="progress-dot"></span>Experimental Design in R</a></li><li data-subkey="sec2sub5"><a href="/Factorial-Experiments-in-R.html"><span class="progress-dot"></span>Factorial Designs (2^k)</a></li><li data-subkey="sec2sub5"><a href="/AB-Testing-in-R.html"><span class="progress-dot"></span>A/B Testing</a></li><li data-subkey="sec2sub5"><a href="/MANOVA-in-R.html"><span class="progress-dot"></span>MANOVA</a></li><li data-subkey="sec2sub5"><a href="/Mixed-ANOVA-in-R.html"><span class="progress-dot"></span>Mixed ANOVA</a></li><li data-subkey="sec2sub5"><a href="/Multivariate-Statistics-in-R.html"><span class="progress-dot"></span>Multivariate Distances &amp; Hotelling's T²</a></li><li data-subkey="sec2sub5"><a href="/PCA-in-R.html"><span class="progress-dot"></span>PCA with prcomp()</a></li><li data-subkey="sec2sub5"><a href="/Interpreting-PCA-Results-in-R.html"><span class="progress-dot"></span>Interpreting PCA Output</a></li><li data-subkey="sec2sub5"><a href="/Exploratory-Factor-Analysis-in-R.html"><span class="progress-dot"></span>Exploratory Factor Analysis</a></li><li data-subkey="sec2sub5"><a href="/CFA-and-Structural-Equation-Modeling-in-R.html"><span class="progress-dot"></span>SEM and CFA (lavaan)</a></li><li data-subkey="sec2sub5"><a href="/Linear-Discriminant-Analysis-in-R.html"><span class="progress-dot"></span>LDA (Linear Discriminant Analysis)</a></li><li data-subkey="sec2sub5"><a href="/Cluster-Analysis-in-R.html"><span class="progress-dot"></span>Clustering (k-Means / HC / DBSCAN)</a></li><li data-subkey="sec2sub5"><a href="/Correspondence-Analysis-in-R.html"><span class="progress-dot"></span>Correspondence Analysis</a></li><li data-subkey="sec2sub5"><a href="/t-SNE-and-UMAP-in-R.html"><span class="progress-dot"></span>t-SNE and UMAP</a></li><li data-subkey="sec2sub5"><a href="/Simple-Linear-Regression-in-R.html"><span class="progress-dot"></span>Simple Linear Regression</a></li><li data-subkey="sec2sub5"><a href="/Multiple-Regression-in-R.html"><span class="progress-dot"></span>Multiple Regression</a></li><li data-subkey="sec2sub5"><a href="/Robust-Regression-in-R.html"><span class="progress-dot"></span>Robust Regression (rlm)</a></li><li data-subkey="sec2sub5"><a href="/factoextra-and-FactoMineR.html"><span class="progress-dot"></span>factoextra (PCA + Clusters)</a></li><li data-subkey="sec2sub5"><a href="/Categorical-Data-in-R.html"><span class="progress-dot"></span>Categorical Data (Tables &amp; Mosaic)</a></li><li data-subkey="sec2sub5"><a href="/Chi-Square-Test-of-Independence-in-R.html"><span class="progress-dot"></span>Chi-Square Test of Independence</a></li><li data-subkey="sec2sub5"><a href="/Chi-Square-Goodness-of-Fit-Test-in-R.html"><span class="progress-dot"></span>Chi-Square Goodness-of-Fit</a></li><li data-subkey="sec2sub5"><a href="/Fishers-Exact-Test-in-R.html"><span class="progress-dot"></span>Fisher's Exact Test</a></li><li data-subkey="sec2sub5"><a href="/Odds-Ratios-and-Relative-Risk-in-R.html"><span class="progress-dot"></span>Odds Ratios &amp; Relative Risk</a></li><li data-subkey="sec2sub5"><a href="/Logistic-Regression-in-R-2.html"><span class="progress-dot"></span>Logistic Regression (Diagnostics)</a></li><li data-subkey="sec2sub5"><a href="/Poisson-and-Negative-Binomial-Regression.html"><span class="progress-dot"></span>Poisson &amp; Negative Binomial Regression</a></li><li data-subkey="sec2sub5"><a href="/Multinomial-and-Ordinal-Logistic-Regression-in-R.html"><span class="progress-dot"></span>Multinomial &amp; Ordinal Logistic Regression</a></li><li data-subkey="sec2sub5"><a href="/When-to-Use-Nonparametric-Tests-in-R.html"><span class="progress-dot"></span>When to Use Nonparametric Tests</a></li><li data-subkey="sec2sub5"><a href="/Wilcoxon-Signed-Rank-Test-in-R.html"><span class="progress-dot"></span>Wilcoxon Signed-Rank Test</a></li><li data-subkey="sec2sub5"><a href="/Mann-Whitney-U-Test-in-R.html"><span class="progress-dot"></span>Mann-Whitney U Test</a></li><li data-subkey="sec2sub5"><a href="/Kruskal-Wallis-Test-in-R-2.html"><span class="progress-dot"></span>Kruskal-Wallis Test</a></li><li data-subkey="sec2sub5"><a href="/Friedman-Test-in-R.html"><span class="progress-dot"></span>Friedman Test</a></li><li data-subkey="sec2sub5"><a href="/Spearman-and-Kendall-Correlation-in-R.html"><span class="progress-dot"></span>Spearman &amp; Kendall Correlation</a></li><li data-subkey="sec2sub5"><a href="/Bootstrap-in-R.html"><span class="progress-dot"></span>Bootstrap (boot package)</a></li><li data-subkey="sec2sub5"><a href="/Quantile-Regression-in-R-2.html"><span class="progress-dot"></span>Quantile Regression</a></li><li data-subkey="sec2sub5"><a href="/Matrix-Operations-in-R.html"><span class="progress-dot"></span>Matrix Operations in R</a></li><li data-subkey="sec2sub5"><a href="/Solving-Linear-Systems-in-R.html"><span class="progress-dot"></span>Solving Linear Systems in R</a></li><li data-subkey="sec2sub5"><a href="/Eigenvalues-and-Eigenvectors-in-R.html"><span class="progress-dot"></span>Eigenvalues &amp; Eigenvectors in R</a></li><li data-subkey="sec2sub5"><a href="/Singular-Value-Decomposition-in-R.html"><span class="progress-dot"></span>Singular Value Decomposition in R</a></li><li data-subkey="sec2sub5"><a href="/Projections-and-the-Hat-Matrix-in-R.html"><span class="progress-dot"></span>Projections &amp; the Hat Matrix</a></li><li data-subkey="sec2sub5"><a href="/QR-Decomposition-in-R.html"><span class="progress-dot"></span>QR Decomposition in R</a></li><li data-subkey="sec2sub5"><a href="/Quadratic-Forms-in-R.html"><span class="progress-dot"></span>Quadratic Forms</a></li><li data-subkey="sec2sub5"><a href="/Matrix-Derivatives-and-the-Hessian-in-R.html"><span class="progress-dot"></span>Matrix Derivatives &amp; Hessian</a></li><li data-subkey="sec2sub5"><a href="/Exponential-Family-Distributions-in-R.html"><span class="progress-dot"></span>Exponential Family Distributions</a></li><li data-subkey="sec2sub5"><a href="/Sufficient-Statistics-in-R.html"><span class="progress-dot"></span>Sufficient Statistics</a></li><li data-subkey="sec2sub5"><a href="/Complete-and-Ancillary-Statistics-in-R.html"><span class="progress-dot"></span>Complete &amp; Ancillary Statistics</a></li><li data-subkey="sec2sub5"><a href="/UMVUE-in-R-2.html"><span class="progress-dot"></span>UMVUE (Rao-Blackwell &amp; Lehmann-Scheffé)</a></li><li data-subkey="sec2sub5"><a href="/Cramer-Rao-Lower-Bound-in-R-2.html"><span class="progress-dot"></span>Cramér-Rao Lower Bound</a></li><li data-subkey="sec2sub5"><a href="/Asymptotic-Theory-in-R-2.html"><span class="progress-dot"></span>Asymptotic Theory</a></li><li data-subkey="sec2sub5"><a href="/Neyman-Pearson-Lemma-in-R-2.html"><span class="progress-dot"></span>Neyman-Pearson Lemma</a></li><li data-subkey="sec2sub5"><a href="/Likelihood-Ratio-Tests-and-Pivotal-Methods.html"><span class="progress-dot"></span>Likelihood Ratio &amp; Pivotal Methods</a></li><li data-subkey="sec2sub5"><a href="/Decision-Theory-in-R.html"><span class="progress-dot"></span>Decision Theory</a></li><li data-subkey="sec2sub5"><a href="/Asymptotic-Relative-Efficiency-in-R.html"><span class="progress-dot"></span>Asymptotic Relative Efficiency</a></li><li data-subkey="sec2sub5"><a href="/Bayes-Theorem-in-R.html"><span class="progress-dot"></span>Bayes' Theorem</a></li><li data-subkey="sec2sub5"><a href="/Bayesian-Statistics-in-R.html"><span class="progress-dot"></span>Bayesian Statistics</a></li><li data-subkey="sec2sub5"><a href="/Conjugate-Priors-in-R.html"><span class="progress-dot"></span>Conjugate Priors</a></li><li data-subkey="sec2sub5"><a href="/Grid-Approximation-in-R.html"><span class="progress-dot"></span>Grid Approximation</a></li><li data-subkey="sec2sub5"><a href="/MCMC-in-R.html"><span class="progress-dot"></span>MCMC in R</a></li><li data-subkey="sec2sub5"><a href="/Gibbs-Sampling-in-R.html"><span class="progress-dot"></span>Gibbs Sampling</a></li><li data-subkey="sec2sub5"><a href="/Hamiltonian-Monte-Carlo-in-R.html"><span class="progress-dot"></span>Hamiltonian Monte Carlo</a></li><li data-subkey="sec2sub5"><a href="/Stan-in-R.html"><span class="progress-dot"></span>Stan</a></li><li data-subkey="sec2sub5"><a href="/brms-in-R.html"><span class="progress-dot"></span>brms</a></li><li data-subkey="sec2sub5"><a href="/Choosing-Priors-in-R.html"><span class="progress-dot"></span>Choosing Priors</a></li><li data-subkey="sec2sub5"><a href="/Prior-Predictive-Checks-in-R.html"><span class="progress-dot"></span>Prior Predictive Checks</a></li><li data-subkey="sec2sub5"><a href="/Compare-Bayesian-Models-in-R.html"><span class="progress-dot"></span>Compare Bayesian Models</a></li><li data-subkey="sec2sub5"><a href="/Posterior-Predictive-Checks-in-R.html"><span class="progress-dot"></span>Posterior Predictive Checks</a></li><li data-subkey="sec2sub5"><a href="/Bayesian-Linear-Regression-in-R.html"><span class="progress-dot"></span>Bayesian Linear Regression</a></li><li data-subkey="sec2sub5"><a href="/Bayesian-Logistic-Regression-in-R.html"><span class="progress-dot"></span>Bayesian Logistic Regression</a></li><li data-subkey="sec2sub5"><a href="/Bayesian-Hierarchical-Models-in-R.html"><span class="progress-dot"></span>Bayesian Hierarchical Models</a></li><li data-subkey="sec2sub5"><a href="/Multilevel-Models-in-R.html"><span class="progress-dot"></span>Multilevel Models</a></li><li data-subkey="sec2sub5"><a href="/Bayesian-ANOVA-in-R.html"><span class="progress-dot"></span>Bayesian ANOVA</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub6" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Machine Learning</li><li data-subkey="sec2sub6"><a href="/Random-Forest-Course.html"><span class="progress-dot"></span>Random Forests (Course)</a></li><li data-subkey="sec2sub6"><a href="/R-Gradient-Boosting-Course.html"><span class="progress-dot"></span>Gradient Boosting (Course)</a></li><li data-subkey="sec2sub6"><a href="/R-tidymodels-Course.html"><span class="progress-dot"></span>tidymodels (Course)</a></li><li data-subkey="sec2sub6" class="is-quiz"><a href="/Machine-Learning-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec2sub6"><a href="/T-Test-Course.html"><span class="progress-dot"></span>The t-test (Lesson)</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">&#9656;</span><span class="sec-num">4.</span> <span class="sec-title-t">Visualization</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub1" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> ggplot2 Foundations</li><li data-subkey="sec3sub1"><a href="/ggplot2-Grammar-of-Graphics.html"><span class="progress-dot"></span>Grammar of Graphics</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Getting-Started.html"><span class="progress-dot"></span>ggplot2 Getting Started</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Aesthetics-aes-Map-Data.html"><span class="progress-dot"></span>ggplot2 Aesthetics (aes)</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Colours.html"><span class="progress-dot"></span>ggplot2 Colours</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Scales.html"><span class="progress-dot"></span>ggplot2 Scales</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Themes-in-R.html"><span class="progress-dot"></span>ggplot2 Themes</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Labels-and-Annotations.html"><span class="progress-dot"></span>Labels &amp; Annotations</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Facets.html"><span class="progress-dot"></span>ggplot2 Facets</a></li><li data-subkey="sec3sub1" class="is-quiz"><a href="/ggplot2-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub2" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Core Charts</li><li data-subkey="sec3sub2"><a href="/ggplot2-Scatter-Plots.html"><span class="progress-dot"></span>Scatter Plots</a></li><li data-subkey="sec3sub2"><a href="/ggplot2-Line-Charts.html"><span class="progress-dot"></span>Line Charts</a></li><li data-subkey="sec3sub2"><a href="/ggplot2-Bar-Charts.html"><span class="progress-dot"></span>Bar Charts</a></li><li data-subkey="sec3sub2"><a href="/ggplot2-Distribution-Charts.html"><span class="progress-dot"></span>Distribution Charts</a></li><li data-subkey="sec3sub2"><a href="/Error-Bars-in-R.html"><span class="progress-dot"></span>Error Bars</a></li><li data-subkey="sec3sub2"><a href="/geom_smooth-in-R.html"><span class="progress-dot"></span>geom_smooth()</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub3" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Distributions &amp; Groups</li><li data-subkey="sec3sub3"><a href="/Violin-Plot-in-R.html"><span class="progress-dot"></span>Violin Plot</a></li><li data-subkey="sec3sub3"><a href="/Ridgeline-Plot-in-R.html"><span class="progress-dot"></span>Ridgeline Plot</a></li><li data-subkey="sec3sub3"><a href="/Lollipop-Chart-in-R.html"><span class="progress-dot"></span>Lollipop Chart</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub4" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Relationships</li><li data-subkey="sec3sub4"><a href="/Bubble-Chart-in-R.html"><span class="progress-dot"></span>Bubble Chart</a></li><li data-subkey="sec3sub4"><a href="/Heatmap-in-R.html"><span class="progress-dot"></span>Heatmap in R</a></li><li data-subkey="sec3sub4"><a href="/Correlation-Matrix-Plot-in-R.html"><span class="progress-dot"></span>Correlation Matrix</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub5" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Advanced Charts</li><li data-subkey="sec3sub5"><a href="/Pie-Donut-Chart-in-R.html"><span class="progress-dot"></span>Pie &amp; Donut Chart</a></li><li data-subkey="sec3sub5"><a href="/Treemap-in-R.html"><span class="progress-dot"></span>Treemap</a></li><li data-subkey="sec3sub5"><a href="/Waffle-Chart-in-R.html"><span class="progress-dot"></span>Waffle Chart</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub6" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Exploratory Analysis</li><li data-subkey="sec3sub6"><a href="/Exploratory-Data-Analysis-in-R.html"><span class="progress-dot"></span>EDA (7-Step Framework)</a></li><li data-subkey="sec3sub6"><a href="/Univariate-EDA-in-R.html"><span class="progress-dot"></span>Univariate EDA</a></li><li data-subkey="sec3sub6"><a href="/Bivariate-EDA-in-R.html"><span class="progress-dot"></span>Bivariate EDA</a></li><li data-subkey="sec3sub6"><a href="/Descriptive-Statistics-in-R.html"><span class="progress-dot"></span>Descriptive Statistics</a></li><li data-subkey="sec3sub6"><a href="/Correlation-Analysis-in-R.html"><span class="progress-dot"></span>Correlation Analysis</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub7" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Interactive &amp; Maps</li><li data-subkey="sec3sub7"><a href="/Combining-ggplot2-with-plotly.html"><span class="progress-dot"></span>ggplot2 + plotly Interactive</a></li><li data-subkey="sec3sub7"><a href="/Interactive-Maps-in-R-with-leaflet.html"><span class="progress-dot"></span>Leaflet Interactive Maps</a></li><li data-subkey="sec3sub7"><a href="/Spatial-Data-in-R-with-sf.html"><span class="progress-dot"></span>Spatial Data (sf)</a></li><li data-subkey="sec3sub7"><a href="/Choropleth-Maps-in-R.html"><span class="progress-dot"></span>Choropleth Maps (sf)</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub8" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Customization &amp; Reference</li><li data-subkey="sec3sub8"><a href="/ggplot2-Legends-in-R.html"><span class="progress-dot"></span>ggplot2 Legends</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Secondary-Axis.html"><span class="progress-dot"></span>Secondary Axis</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Log-Scale.html"><span class="progress-dot"></span>Log Scale</a></li><li data-subkey="sec3sub8"><a href="/patchwork-Package.html"><span class="progress-dot"></span>patchwork (Combine Plots)</a></li><li data-subkey="sec3sub8"><a href="/Publication-Quality-Figures-in-R.html"><span class="progress-dot"></span>Publication-Ready Figures</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-cheatsheet.html"><span class="progress-dot"></span>ggplot2 Quickref</a></li><li data-subkey="sec3sub8"><a href="/Advanced-ggplot2-Course.html"><span class="progress-dot"></span>Advanced ggplot2 (Course)</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Course.html"><span class="progress-dot"></span>ggplot2 (Course)</a></li><li data-subkey="sec3sub8"><a href="/Dashboards-Course.html"><span class="progress-dot"></span>Interactive Dashboards (Course)</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">&#9656;</span><span class="sec-num">5.</span> <span class="sec-title-t">Time Series</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li data-subkey="sec4sub0"><a href="/Time-Series-Analysis-With-R.html"><span class="progress-dot"></span>Time Series Analysis</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Forecasting-With-R.html"><span class="progress-dot"></span>Time Series Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Forecasting-With-R-part2.html"><span class="progress-dot"></span>More Time Series Forecasting</a></li><li data-subkey="sec4sub0" class="is-quiz"><a href="/Time-Series-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">&#9656;</span><span class="sec-num">6.</span> <span class="sec-title-t">Advanced R</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub1" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Functional Programming</li><li data-subkey="sec5sub1"><a href="/Functional-Programming-in-R.html"><span class="progress-dot"></span>Functional Programming</a></li><li data-subkey="sec5sub1" class="is-quiz"><a href="/R-Functional-Programming-Exercises-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec5sub1"><a href="/purrr-map-Variants.html"><span class="progress-dot"></span>purrr map() Variants</a></li><li data-subkey="sec5sub1"><a href="/R-Anonymous-Functions.html"><span class="progress-dot"></span>R Anonymous Functions</a></li><li data-subkey="sec5sub1"><a href="/R-Function-Factories.html"><span class="progress-dot"></span>R Function Factories</a></li><li data-subkey="sec5sub1"><a href="/R-Function-Operators.html"><span class="progress-dot"></span>R Function Operators</a></li><li data-subkey="sec5sub1"><a href="/Reduce-Filter-Map-in-R.html"><span class="progress-dot"></span>Reduce, Filter, Map</a></li><li data-subkey="sec5sub1"><a href="/Memoization-in-R.html"><span class="progress-dot"></span>Memoization in R</a></li><li data-subkey="sec5sub1"><a href="/Writing-Composable-R-Code.html"><span class="progress-dot"></span>Composable R Code</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub2" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> OOP in R</li><li data-subkey="sec5sub2"><a href="/OOP-in-R.html"><span class="progress-dot"></span>OOP in R: S3/S4/R6</a></li><li data-subkey="sec5sub2"><a href="/S3-Classes-in-R.html"><span class="progress-dot"></span>S3 Classes</a></li><li data-subkey="sec5sub2"><a href="/S3-Method-Dispatch-in-R.html"><span class="progress-dot"></span>S3 Method Dispatch</a></li><li data-subkey="sec5sub2"><a href="/S4-Classes-in-R.html"><span class="progress-dot"></span>S4 Classes</a></li><li data-subkey="sec5sub2"><a href="/S4-Methods-in-R.html"><span class="progress-dot"></span>S4 Methods &amp; Dispatch</a></li><li data-subkey="sec5sub2"><a href="/R6-Classes-in-R.html"><span class="progress-dot"></span>R6 Classes</a></li><li data-subkey="sec5sub2"><a href="/R6-Advanced.html"><span class="progress-dot"></span>R6 Advanced</a></li><li data-subkey="sec5sub2"><a href="/Operator-Overloading-in-R.html"><span class="progress-dot"></span>Operator Overloading</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub3" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> How R Works</li><li data-subkey="sec5sub3"><a href="/R-Names-and-Values.html"><span class="progress-dot"></span>R Names &amp; Values</a></li><li data-subkey="sec5sub3"><a href="/R-Assignment-Deep-Dive.html"><span class="progress-dot"></span>R Assignment Deep Dive</a></li><li data-subkey="sec5sub3"><a href="/R-Memory-lobstr.html"><span class="progress-dot"></span>R Memory &amp; lobstr</a></li><li data-subkey="sec5sub3"><a href="/R-Environments.html"><span class="progress-dot"></span>R Environments</a></li><li data-subkey="sec5sub3"><a href="/R-Lexical-Scoping.html"><span class="progress-dot"></span>Lexical Scoping</a></li><li data-subkey="sec5sub3"><a href="/R-Closures.html"><span class="progress-dot"></span>R Closures</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub4" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Debugging &amp; Performance</li><li data-subkey="sec5sub4"><a href="/R-Conditions-System.html"><span class="progress-dot"></span>Conditions System</a></li><li data-subkey="sec5sub4"><a href="/R-Debugging.html"><span class="progress-dot"></span>Debugging R Code</a></li><li data-subkey="sec5sub4"><a href="/R-Common-Errors.html"><span class="progress-dot"></span>50 Common R Errors</a></li><li data-subkey="sec5sub4"><a href="/Parallel-Computing-With-R.html"><span class="progress-dot"></span>Parallel Computing</a></li><li data-subkey="sec5sub4"><a href="/Strategies-To-Improve-And-Speedup-R-Code.html"><span class="progress-dot"></span>Speedup R Code</a></li><li data-subkey="sec5sub4" class="is-quiz"><a href="/Shiny-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">&#9656;</span><span class="sec-num">7.</span> <span class="sec-title-t">Classic Tutorials</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li data-subkey="sec6sub0"><a href="/R-Tutorial.html"><span class="progress-dot"></span>R Tutorial (Classic)</a></li><li data-subkey="sec6sub0"><a href="/ggplot2-Tutorial-With-R.html"><span class="progress-dot"></span>ggplot2 Short Tutorial</a></li><li data-subkey="sec6sub0"><a href="/Complete-Ggplot2-Tutorial-Part1-With-R-Code.html"><span class="progress-dot"></span>ggplot2 Tutorial 1 - Intro</a></li><li data-subkey="sec6sub0"><a href="/Complete-Ggplot2-Tutorial-Part2-Customizing-Theme-With-R-Code.html"><span class="progress-dot"></span>ggplot2 Tutorial 2 - Theme</a></li><li data-subkey="sec6sub0"><a href="/Top50-Ggplot2-Visualizations-MasterList-R-Code.html"><span class="progress-dot"></span>ggplot2 Tutorial 3 - Masterlist</a></li><li data-subkey="sec6sub0"><a href="/Association-Mining-With-R.html"><span class="progress-dot"></span>Association Mining</a></li><li data-subkey="sec6sub0"><a href="/Multi-Dimensional-Scaling-With-R.html"><span class="progress-dot"></span>Multi Dimensional Scaling</a></li><li data-subkey="sec6sub0"><a href="/Optimization-With-R.html"><span class="progress-dot"></span>Optimization</a></li><li data-subkey="sec6sub0"><a href="/Information-Value-With-R.html"><span class="progress-dot"></span>InformationValue Package</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">&#9656;</span><span class="sec-num">8.</span> <span class="sec-title-t">Practice Exercises</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec7sub1" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Mastery Quizzes (Certificate)</li><li data-subkey="sec7sub1" class="is-quiz"><a href="/R-Beginner-Exercises-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub1" class="is-quiz"><a href="/dplyr-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub1" class="is-quiz"><a href="/ggplot2-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub1" class="is-quiz"><a href="/Hypothesis-Testing-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub1" class="is-quiz"><a href="/Linear-Regression-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub1" class="is-quiz"><a href="/Machine-Learning-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub1" class="is-quiz"><a href="/tidyr-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub1" class="is-quiz"><a href="/Time-Series-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub1" class="is-quiz"><a href="/Shiny-Exercises-in-R-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub1" class="is-quiz"><a href="/R-Interview-Questions-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub1" class="is-quiz"><a href="/R-Functional-Programming-Exercises-quiz.html"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec7sub2" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> R Fundamentals</li><li data-subkey="sec7sub2"><a href="/R-Basics-Exercises.html"><span class="progress-dot"></span>R Basics (15 problems)</a></li><li data-subkey="sec7sub2"><a href="/R-Vectors-Exercises.html"><span class="progress-dot"></span>R Vectors (12 problems)</a></li><li data-subkey="sec7sub2"><a href="/R-Data-Frames-Exercises.html"><span class="progress-dot"></span>R Data Frames (15 problems)</a></li><li data-subkey="sec7sub2"><a href="/R-Lists-Exercises.html"><span class="progress-dot"></span>R Lists (10 problems)</a></li><li data-subkey="sec7sub2"><a href="/R-Control-Flow-Exercises.html"><span class="progress-dot"></span>R Control Flow (12 problems)</a></li><li data-subkey="sec7sub2"><a href="/R-Functions-Exercises.html"><span class="progress-dot"></span>R Functions (10 problems)</a></li><li data-subkey="sec7sub2"><a href="/R-String-Exercises.html"><span class="progress-dot"></span>R Strings (10 problems)</a></li><li data-subkey="sec7sub2"><a href="/R-Date-Time-Exercises.html"><span class="progress-dot"></span>R Date &amp; Time (10 problems)</a></li><li data-subkey="sec7sub2"><a href="/R-Apply-Exercises.html"><span class="progress-dot"></span>R apply Family (12 problems)</a></li><li data-subkey="sec7sub2"><a href="/R-Subsetting-Exercises.html"><span class="progress-dot"></span>R Subsetting (10 problems)</a></li><li data-subkey="sec7sub2"><a href="/R-Functional-Programming-Exercises.html"><span class="progress-dot"></span>Functional Programming (10 problems)</a></li><li data-subkey="sec7sub2"><a href="/R-OOP-Exercises.html"><span class="progress-dot"></span>OOP in R (8 problems)</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec7sub3" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Data Wrangling</li><li data-subkey="sec7sub3"><a href="/R-Data-Import-Exercises.html"><span class="progress-dot"></span>Data Import (10 problems)</a></li><li data-subkey="sec7sub3"><a href="/dplyr-Exercises.html"><span class="progress-dot"></span>dplyr (15 problems)</a></li><li data-subkey="sec7sub3"><a href="/dplyr-filter-select-Exercises.html"><span class="progress-dot"></span>dplyr filter() &amp; select() (12 problems)</a></li><li data-subkey="sec7sub3"><a href="/dplyr-group-by-summarise-Exercises.html"><span class="progress-dot"></span>dplyr group_by() &amp; summarise() (10 problems)</a></li><li data-subkey="sec7sub3"><a href="/dplyr-Join-Exercises.html"><span class="progress-dot"></span>dplyr Joins (10 problems)</a></li><li data-subkey="sec7sub3"><a href="/data-table-Exercises.html"><span class="progress-dot"></span>data.table (12 problems)</a></li><li data-subkey="sec7sub3"><a href="/purrr-Exercises.html"><span class="progress-dot"></span>purrr (10 problems)</a></li><li data-subkey="sec7sub3"><a href="/tidyr-Reshaping-Exercises.html"><span class="progress-dot"></span>tidyr Reshaping (10 problems)</a></li><li data-subkey="sec7sub3"><a href="/Missing-Data-in-R-Exercises.html"><span class="progress-dot"></span>Missing Data in R (10 problems)</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec7sub4" data-collapsed="false"><span class="subsec-chevron">&#9660;</span> Visualization</li><li data-subkey="sec7sub4"><a href="/ggplot2-Exercises.html"><span class="progress-dot"></span>ggplot2 (15 problems)</a></li><li data-subkey="sec7sub4"><a href="/ggplot2-Geom-Exercises.html"><span class="progress-dot"></span>ggplot2 Geoms (12 problems)</a></li><li data-subkey="sec7sub4"><a href="/ggplot2-Aesthetics-Exercises.html"><span class="progress-dot"></span>ggplot2 Aesthetics (10 problems)</a></li><li data-subkey="sec7sub4"><a href="/ggplot2-Customization-Exercises.html"><span class="progress-dot"></span>ggplot2 Customization (10 problems)</a></li><li 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          <blockquote>
<p>Beta regression is commonly used when you want to model <span class="math inline"><em>Y</em></span> that are probabilities themselves.</p>
</blockquote>
<p>This is evident when the value of <span class="math inline"><em>Y</em></span> is a <em>proportion</em> that ranges between 0 to 1. The data points of <span class="math inline"><em>Y</em></span> variable typically represent a proportion of events that form a subset of the total population (assuming that it follows a beta distribution).</p>
<h2>Use Cases</h2>
<ol style="list-style-type: decimal">
<li>From GasolineYield data: Proportion of crude oil converted to gasoline after distillation and fractionation</li>
<li>Proportion of individuals infected with ‘xyz’ when exposed to various levels of artificial preservative agent.</li>
</ol>
<h2>Example: Gasoline Yield</h2>
<p>Lets predict the gasoline <code>yield</code> as a function of <code>batch</code> and temperature. The example below shows an example implementation of beta regression using the GasolineYield data from <code>betareg</code> package.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span> (betareg)
<span class="kw">data</span>(<span class="st">&quot;GasolineYield&quot;</span>, <span class="dt">package =</span> <span class="st">&quot;betareg&quot;</span>)  <span class="co"># initialize data</span>
inputData &lt;-<span class="st"> </span>GasolineYield  <span class="co"># plug-in your data here</span>
trainingIndex &lt;-<span class="st"> </span><span class="kw">c</span>(<span class="dv">1</span>:(<span class="kw">nrow</span>(inputData)-<span class="dv">1</span>))  <span class="co"># create row indices of training data</span>
trainingData &lt;-<span class="st"> </span>inputData[trainingIndex, ] <span class="co"># training data</span>
testData &lt;-<span class="st"> </span>inputData[-trainingIndex, ] <span class="co"># test data</span>
betaMod &lt;-<span class="st"> </span><span class="kw">betareg</span>(yield ~<span class="st"> </span>batch +<span class="st"> </span>temp, <span class="dt">data =</span> trainingData) <span class="co"># train model. Tune var names.</span>
<span class="kw">summary</span> (betaMod) <span class="co"># model summary</span>
<span class="kw">predict</span> (betaMod, testData) <span class="co"># predict on test data (0.19 vs actual 0.18)</span>

<span class="co">#&gt; Call:</span>
<span class="co">#&gt; betareg(formula = yield ~ batch + temp, data = GasolineYield)</span>
<span class="co">#&gt; </span>
<span class="co">#&gt; Standardized weighted residuals 2:</span>
<span class="co">#&gt;     Min      1Q  Median      3Q     Max </span>
<span class="co">#&gt; -2.8750 -0.8149  0.1601  0.8384  2.0483 </span>
<span class="co">#&gt; </span>
<span class="co">#&gt; Coefficients (mean model with logit link):</span>
<span class="co">#&gt;               Estimate Std. Error z value Pr(&gt;|z|)    </span>
<span class="co">#&gt; (Intercept) -6.1595710  0.1823247 -33.784  &lt; 2e-16 </span>
<span class="co">#&gt; batch1       1.7277289  0.1012294  17.067  &lt; 2e-16 </span>
<span class="co">#&gt; batch2       1.3225969  0.1179020  11.218  &lt; 2e-16 </span>
<span class="co">#&gt; batch3       1.5723099  0.1161045  13.542  &lt; 2e-16 </span>
<span class="co">#&gt; batch4       1.0597141  0.1023598  10.353  &lt; 2e-16 </span>
<span class="co">#&gt; batch5       1.1337518  0.1035232  10.952  &lt; 2e-16 </span>
<span class="co">#&gt; batch6       1.0401618  0.1060365   9.809  &lt; 2e-16 </span>
<span class="co">#&gt; batch7       0.5436922  0.1091275   4.982 6.29e-07 </span>
<span class="co">#&gt; batch8       0.4959007  0.1089257   4.553 5.30e-06 </span>
<span class="co">#&gt; batch9       0.3857930  0.1185933   3.253  0.00114 ** </span>
<span class="co">#&gt; temp         0.0109669  0.0004126  26.577  &lt; 2e-16 </span>
<span class="co">#&gt; </span>
<span class="co">#&gt; Phi coefficients (precision model with identity link):</span>
<span class="co">#&gt;       Estimate Std. Error z value Pr(&gt;|z|)    </span>
<span class="co">#&gt; (phi)    440.3      110.0   4.002 6.29e-05 </span>
<span class="co">#&gt; </span>
<span class="co">#&gt; Signif. codes:  0 &#39;&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 </span>
<span class="co">#&gt; </span>
<span class="co">#&gt; Type of estimator: ML (maximum likelihood)</span>
<span class="co">#&gt; Log-likelihood:  84.8 on 12 Df</span>
<span class="co">#&gt; Pseudo R-squared: 0.9617</span>
<span class="co">#&gt; Number of iterations: 51 (BFGS) + 3 (Fisher scoring)</span></code></pre></div>
<p>This page is based on the examples available in <a href="http://cran.r-project.org/web/packages/betareg/vignettes/betareg.pdf">Beta regression vignette</a>.</p>


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