## Logistic Regression

Fit a logistic regression model with a single quantitative predictor. Obtain parameter estimates, a graph of the fitted probabilities and construct confidence intervals.

## Compare Two Means

Confidence interval and significance test for the difference of two means. Independent & dependent samples.

Coming soon ...

## Normal Distribution

Explore how mean and standard deviation change the shape and find percentiles (critical values) or probabilities.

## Binomial Distribution

Find the probability for the number of successes in n Bernoulli trials. Explore how the distribution depends on n and p.

# Distributions: Explore the Shape, Find Probabilities and Percentiles

## Time Series

Plot a simple time series and add a smooth or linear trend.

## Random Numbers

Generate random numbers or flips of a (biased) coin. Keep track of generated numbers with a bar chart.

# ​​Exploratory Analysis (One and Two Samples), Random Numbers

## F Distribution

Explore how the shape depends on the two sets of degrees of freedom. Find and visualize percentiles and probabilities.

## Inference for a Mean

Find confidence intervals and test hypo-theses about a population mean. Visualize the interval or P-value.

# Sampling Distributions and the Central Limit Theorem

## t Distribution

Explore how the degrees of freedom effect the shape and find percentiles, probabilities and P-values STATISTICS

THE ART & SCIENCE OF LEARNING FROM DATA

AGRESTI  ·  FRANKLIN  ·  KLINGENBERG

## Nonparametric Tests

In the meantime, the Boostrap for One Samples can do the Wilcoxon Test.

## Compare Two Proportions

Confidence interval and significance test for the difference of two proportions. Independent & dependent samples.

## Chi-Squared Distribution

Explore how the shape depends on the degrees of freedom. Find and visualize percentiles and probabilities.

## Scatterplots & Correlation

Construct interactive scatterplots, hover over points, move them around or overlay a smooth trend line. Find the correlation coefficient r. Built the sampling distribution of r via bootstrapping or permutation, one resample at a time.

## Exponential Regression

Fit and visualize a simple exponential regression model to data such as the number of COVID-19 infections in New York City in March 2020 (Example 16, Chapter 13).

## Chi-squared Test

Test for independence, homogeneity or goodness of fit in contingency tables. Analyze observed & expected counts and residuals.

## Inference for a Proportion

Find confidence intervals and test hypo-theses about a population proportion. Visualize the interval or P-value.

For continuous variables. Choose from many different population distributions (or built your own) and explore the sampling distribution.

# Interactive Web Apps

## Bootstrap for One Sample

Create the bootstrap distribution of the mean, median or standard deviation and find the percentile confidence interval.

Visualize and run a permutation test for testing independence in a contingency table using Pearson's Chi-squared statistic.

See how the sampling distribution builds up with repeated sampling and explore how its shape depends on n and p.

## Categorical Variables

Construct 2x2 contingency tables, obtain conditional proportions and get a bar graph. Find the difference or ratio of proportions. Built the sampling distribution via resampling.

## Poisson Distribution

Explore how the shape of the Poisson Distribution depends on λ and find probabilities of various kinds

## Multiple Linear Regression

In the meantime, use the Multivariate Relationships app, which has some capablities to fit a multiple linear regression model with two explanatory variables.

## Permutation Test

Visualize and run a permutation test comparing two samples with a quantitative response.

## Errors and Power

Explore probabilities of Type I and Type II errors and connections to sample size, significance level and true parameter value.

## Mean vs. Median

Explore the relationship between the mean and median for data coming from a variety of distributions, or enter your own data.

## ANOVA (One-Way)

Analysis of Variance for one factor, including multiple comparisons of means (Tukey, Dunnett). (Under Construction)

# One Sample Inference: Confidence Intervals & Significance Tests

Coming soon ...

For discrete variables. Define your own discrete distribution (such as uniform or skewed) and explore the sampling distribution.

## Explore Categorical Data

Construct frequency and contingency tables and bar graphs to explore distributions of categorical variables. For one or two variables.

## Explore Linear Regression

Create scatterplots from scratch by clicking in an empty plot and creating points. Investigate the effect of outliers on the regression line. Simulate linear or non-linear relationships.

# Bootstrap Confidence Intervals & Permutation Tests

## Guess the Correlation

Randomly generate scatterplots to guess the correlation coefficient r. Optionally, display the regression line. How do your guesses correlate with the actual values?

## Explore Quantitative Data

Find summary statistics and construct inter-active histograms, boxplots, dotplots or stem & leaf plots. For one or several samples.

## Bootstrap for Two Samples

Create the bootstrap distribution for the difference of means or medians, and find percentile confidence intervals.

## Multivariate Relationships

Construct interactive scatterplots to explore the relationship between two quantitative variables while accounting for a third (categorical or quantitative) grouping variable.

## Fisher's Exact Test

Visualize and run Fisher's exact test for

2 x 2 contingency tables.

## Linear Regression

Construct interactive scatterplots and super-impose a regression line. Obtain the regression equation, rr-squared and obtain predictions. Display & analyze residuals.

## Explore Coverage

What does 95% confidence mean? What affects the width of an interval? Visualize with intervals for proportions or means.