Statistics II

Albrecht Gebhardt

Introduction

Statistics

this
that

A classic code snippet

fit = lm(mpg ~ am, data = mtcars)
summary(fit)


Call:
lm(formula = mpg ~ am, data = mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-9.3923 -3.0923 -0.2974  3.2439  9.5077 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   17.147      1.125  15.247 1.13e-15 ***
am             7.245      1.764   4.106 0.000285 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 4.902 on 30 degrees of freedom
Multiple R-squared:  0.3598,    Adjusted R-squared:  0.3385 
F-statistic: 16.86 on 1 and 30 DF,  p-value: 0.000285

The same directly in your Browser

Some LaTeX (MathJAX) Formula

\[\begin{gather*} a_1=b_1+c_1\\ a_2=b_2+c_2-d_2+e_2 \end{gather*}\]

and some more

\[\begin{align} a_{11}& =b_{11}& a_{12}& =b_{12}\\ a_{21}& =b_{21}& a_{22}& =b_{22}+c_{22} \end{align}\]

A Python Shiny App

#| standalone: true
#| viewerHeight: 420

from shiny import App, render, ui
import numpy as np
import matplotlib.pyplot as plt

app_ui = ui.page_fluid(
    ui.layout_sidebar(
        ui.panel_sidebar(
            ui.input_slider("period", "Period", 0.5, 2, 1, step=0.5),
            ui.input_slider("amplitude", "Amplitude", 0, 2, 1, step=0.25),
            ui.input_slider("shift", "Phase shift", 0, 2, 0, step=0.1),
        ),
        ui.panel_main(
            ui.output_plot("plot"),
        ),
    ),
)


def server(input, output, session):
    @output
    @render.plot(alt="Sine function")
    def plot():
        t = np.arange(0.0, 4.0, 0.01)
        s = input.amplitude() * np.sin(
            (2 * np.pi / input.period()) * (t - input.shift() / 2)
        )
        fig, ax = plt.subplots()
        ax.set_ylim([-2, 2])
        ax.plot(t, s)
        ax.grid()


app = App(app_ui, server)