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:bar_chart: Methods of Applied Statistics Course Textbook Repository

Home Page: https://book.stat420.org/

R 0.07% TeX 0.02% CSS 0.21% HTML 99.71%

probability statistics r textbook applied-statistics linear-models bookdown book

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davidunger lightfromdark dmcquillan314 zongyw guagua36 rgjeldum yongkangzhou imiu alokkshukla ddlee6 kfz0131 uppalap2 anhnguyendepocen wen036 cjw237 xiaoxue88 qiqi-kiki luke199629 goodyoyo0214 eloiserosen trexwithoutt mjhihi munsheet xiaojie2 zixin96 nathanael-claussen cxzhang4 floswald zampolli75 qisw hermandr rswaya2 viola17 mesfind jeffgerlach auserj rayfix linuxdream fintrek yifantian sdgdavidd bandhakavi bblrd tdcnguyen sakuraxin ihrushikesh junkim327 jjuhn erickmuthama schrezraoeder cbymar bpatters awasthi pphamnham rajaomalalasendra helixcn doherty-m89 k8dix snowdj pragyamis jonduan kyleholgate mattschley aaronblythe whismura ksezgin80 marcoemorais ko3ak-i3-xopcy gridl csbuja pvsdileep abhishek-badsha enneya mzeybek583 mohamed-180 fmparzen rehanumar afcarl imaheshdivakaran yasinkutuk amrofi andernsm jaeyk aapplepku dipsingh adtossou kogilo seulert sethpoulsen bcarny yiqiao-yin mwickram marcoroy-yx15 forkedrepositories jmatias greenfacts anouel hdocmsu nbalepur surfcao

appliedstats's Issues

Switch over to GH Actions runner

Some steps to be taken:

Disabling .travis.yaml by deleting it
Remove deployment/ folder
Add .github/workflows/bookdown.yaml

Notes:

We'll use a slightly modified bookdown action to avoid reliance on Netlify.
The main website will remain "active", but until the runner builds will not automatically update.
It may be advantageous in non-peak hours to rebuild the gh-pages branch as it contains old artifacts.

bookdown -> quarto

It's time to update this over to using quarto...

https://github.com/coatless-tutorials/quarto-book-template

Multiple Regression ANOVA

Put calculated values into traditional table to bridge gap between R and the usual table.

Correct a typo

On 8.7 "We modify our notation slightly to make it clear that the the predicted value is a function of", there is double words "the", I tested on IE and Chrome, both displayed double "the".

build leave behind a data/example-data.csv file

When you perform a clean build from index.Rmd the file data/example-data.csv shows up as an untracked file.

I would expect things to be clean after a book build.

It looks like there is a very similar and possibly unused file called data/example_data.csv The only difference is between an underbar and a minus.

Linear Algebra

Show sample mean, standard deviation, finding minimum as matrix operations. Inspiration: http://genomicsclass.github.io/book/pages/matrix_algebra_examples.html

RStudio “cheatsheets” in section 6.5 redirects to "Page Not Found"

If you click on the hyperlink RStudio “cheatsheets”in section 6.5, it redirects to an old page which is not present anymore.

The old page URL is:
https://www.rstudio.com/wp-content/uploads/2016/01/rstudio-IDE-cheatsheet.pdf

However, Rstudio seems to have updated this cheatsheet to a new URL, which is as follows:
https://www.rstudio.com/wp-content/uploads/2019/01/Cheatsheets_2019.pdf

This can be easily updated in the r-resources.Rmd file.

Add MLR LS Matrix Specifics

See https://github.com/coatless/stat385/blob/gh-pages/assets/lectures/lec9/lec9-s3-objects-a-study-in-linear-regression.Rmd

Absent are the justification behind the MLR matrix calculations. Within the above deck, I've written out the derivation for an MLR function.

Bolding

Bold Greek characters with MathJax: http://www.onemathematicalcat.org/MathJaxDocumentation/TeXSyntax.htm

Link Targets

Make links to outside domains have target = "_blank"

http://stackoverflow.com/questions/4425198/markdown-target-blank

applied_statistics.rds

The file applied_statistics.rds shows up with version control status when you do a build. Should this file be git ignored?

Provide typo fixing guide

Add guide in #79 (comment) to the front matter with a link in the lower left for "spot a typo?"

Potentially, might want to add in hypothes.is (e.g. a "suggest"/annotation layer.)

RGL Embedded Least Squares / ANOVA Plot

Interactive vs. stagnate plots requires use of rgl

To use with rmarkdown, might need to enable hook_webgl()? Need fallback for pdf version. (JS Error)

open3d()
x = rnorm(100)
y = rnorm(100)
z = 0.2*x - 0.3*y + rnorm(100, sd = 0.3)
fit = lm(z ~ x + y)
plot3d(x, y, z, type = "s", col = "red", size = 1)
coefs = coef(fit)
a = coefs["x"]
b = coefs["y"]
c = -1
d = coefs["(Intercept)"]
planes3d(a, b, c, d, alpha = 0.5)

Better version in car::scatter3d:

http://www.inside-r.org/packages/cran/car/docs/identify3d

See:

http://www.ats.ucla.edu/stat/r/dae/intreg.htm

For anova plot

Categorical x Categorical Interaction

Add Example, Discussion

Table text content

Text content in all tables not center aligned, but header displays are.

RMarkdown LaTeX Syntax

Change \[ \] to $$ $$ where it still exists.

Purl

Seemingly random permissions error when creating .R file. (Quits at random line.)

What should be done for "TODO: coercion" in chapter3

TODO: coercion seems to be left unresolved.

appliedstats/data-and-programming.Rmd

Line 210 in 53b7a49

- TODO: coercion

However, I think there is an explanation for coercion as follows.

appliedstats/data-and-programming.Rmd

Lines 212 to 217 in 53b7a49

    
           ```{r} 
        
           sum(x > 3) 
        
           as.numeric(x > 3) 
        
           ``` 
        
           Here we see that using the `sum()` function on a vector of logical `TRUE` and `FALSE` values that is the result of `x > 3` results in a numeric result. `R` is first automatically coercing the logical to numeric where `TRUE` is `1` and `FALSE` is `0`. This coercion from logical to numeric happens for most mathematical operations.

Should we delete the TODO line or fix something more?

LaTeX equation conversion hiccups under epub

Looks like some equations do not use valid latex for epub.

I think \bf needs to be switched to \boldsymbol{}. Not a show-stopper.

list of equation issues

[WARNING] Could not convert TeX math '
  (\alpha \beta)_{1j} + (\alpha \beta)_{2j} + (\alpha \beta)_{3j} = 0 \\
  (\alpha \beta)_{i1} + (\alpha \beta)_{i2} + (\alpha \beta)_{i3} + (\alpha \beta)_{i4} = 0
  ', rendering as TeX:
  (\alpha \beta)_{1j} + (\alpha \beta)_{2j
  ^
  unexpected "("
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  Y \mid {\bf X} = {\bf x} \sim N(\beta_0 + \beta_1x_1 + \ldots + \beta_{p - 1}x_{p - 1}, \ \sigma^2)
  ', rendering as TeX:
  
              ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\eta({\bf x})', rendering as TeX:
  \eta({\bf x})
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\eta({\bf x}) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \ldots  + \beta_{p - 1} x_{p - 1}', rendering as TeX:
  \eta({\bf x}) = \beta_0 + \beta_1 x_1 + 
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\eta({\bf x})', rendering as TeX:
  \eta({\bf x})
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\text{E}[Y \mid {\bf X} = {\bf x}]', rendering as TeX:
  ext{E}[Y \mid {\bf X} = {\bf x}]
                     ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \eta({\bf x}) = g\left(\text{E}[Y \mid {\bf X} = {\bf x}]\right).
  ', rendering as TeX:
  
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'Y \mid {\bf X} = {\bf x}', rendering as TeX:
  Y \mid {\bf X} = {\bf x}
              ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'N(\mu({\bf x}), \sigma^2)', rendering as TeX:
  N(\mu({\bf x}), \sigma^2)
             ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\text{Pois}(\lambda({\bf x}))', rendering as TeX:
  Pois}(\lambda({\bf x}))
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\text{Bern}(p({\bf x}))', rendering as TeX:
  \text{Bern}(p({\bf x}))
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\text{E}[Y \mid {\bf X} = {\bf x}]', rendering as TeX:
  ext{E}[Y \mid {\bf X} = {\bf x}]
                     ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\mu({\bf x})', rendering as TeX:
  \mu({\bf x})
           ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\lambda({\bf x})', rendering as TeX:
  \lambda({\bf x})
               ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'p({\bf x})', rendering as TeX:
  p({\bf x})
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\eta({\bf x}) = \mu({\bf x})', rendering as TeX:
  \eta({\bf x}) = \mu({\bf x})
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\eta({\bf x}) = \log(\lambda({\bf x}))', rendering as TeX:
  \eta({\bf x}) = \log(\lambda({\bf x}))
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\eta({\bf x}) = \log \left(\frac{p({\bf x})}{1 - p({\bf x})} \right)', rendering as TeX:
  \eta({\bf x}) = \log \left(\frac{p({\bf 
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\mu({\bf x}) = \eta({\bf x})', rendering as TeX:
  \mu({\bf x}) = \eta({\bf x})
           ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\lambda({\bf x}) = e^{\eta({\bf x})}', rendering as TeX:
  \lambda({\bf x}) = e^{\eta({\bf x})}
               ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'p({\bf x}) = \frac{e^{\eta({\bf x})}}{1 + e^{\eta({\bf x})}} = \frac{1}{1 + e^{-\eta({\bf x})}}', rendering as TeX:
  p({\bf x}) = \frac{e^{\eta({\bf x})}}{1 
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\eta({\bf x})', rendering as TeX:
  \eta({\bf x})
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \eta({\bf x}) = g\left(\text{E}[Y \mid {\bf X} = {\bf x}]\right).
  ', rendering as TeX:
  
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \text{E}[Y \mid {\bf X} = {\bf x}] = g^{-1}(\eta({\bf x})).
  ', rendering as TeX:
  
                     ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  p({\bf x}) = P[Y = 1 \mid {\bf X} = {\bf x}]
  ', rendering as TeX:
  
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  P[Y = 0 \mid {\bf X} = {\bf x}] + P[Y = 1 \mid {\bf X} = {\bf x}] = 1
  ', rendering as TeX:
  
                    ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  P[Y = 0 \mid {\bf X} = {\bf x}] = 1 - p({\bf x})
  ', rendering as TeX:
  
                    ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \log\left(\frac{p({\bf x})}{1 - p({\bf x})}\right) = \beta_0 + \beta_1 x_1 + \ldots  + \beta_{p - 1} x_{p - 1}
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \frac{p({\bf x})}{1 - p({\bf x})} = \frac{P[Y = 1 \mid {\bf X} = {\bf x}]}{P[Y = 0 \mid {\bf X} = {\bf x}]}
  ', rendering as TeX:
  
               ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'p({\bf x})', rendering as TeX:
  p({\bf x})
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  Y \mid {\bf X} = {\bf x} \sim N(\beta_0 + \beta_1x_1 + \ldots + \beta_qx_q, \ \sigma^2).
  ', rendering as TeX:
  
              ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'p({\bf x})', rendering as TeX:
  p({\bf x})
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \log\left(\frac{p({\bf x})}{1 - p({\bf x})}\right) = \beta_0 + \beta_1 x_1 + \ldots  + \beta_{q} x_{q}
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'p({\bf x})', rendering as TeX:
  p({\bf x})
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  p({\bf x}) = P[Y = 1 \mid {\bf X} = {\bf x}] = \frac{e^{\beta_0 + \beta_1 x_{1} + \cdots + \beta_{p-1} x_{(p-1)}}}{1 + e^{\beta_0 + \beta_1 x_{1} + \cdots + \beta_{p-1} x_{(p-1)}}}
  ', rendering as TeX:
  
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \log\left(\frac{p({\bf x_i})}{1 - p({\bf x_i)})}\right) = \beta_0 + \beta_1 x_{i1} + \cdots + \beta_{p-1} x_{i(p-1)}
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'P[Y_i = 1 \mid {\bf X_i} = {\bf x_i}]', rendering as TeX:
  [Y_i = 1 \mid {\bf X_i} = {\bf x_i}]
                     ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  p({\bf x_i}) = P[Y_i = 1 \mid {\bf X_i} = {\bf x_i}] = \frac{e^{\beta_0 + \beta_1 x_{i1} + \cdots + \beta_{p-1} x_{i(p-1)}}}{1 + e^{\beta_0 + \beta_1 x_{i1} + \cdots + \beta_{p-1} x_{i(p-1)}}}
  ', rendering as TeX:
  
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  1 - p({\bf x_i}) = P[Y_i = 0 \mid {\bf X} = {\bf x_i}] = \frac{1}{1 + e^{\beta_0 + \beta_1 x_{i1} + \cdots + \beta_{p-1} x_{i(p-1)}}}
  ', rendering as TeX:
  
             ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  L(\boldsymbol{{\beta}}) = \prod_{i = 1}^{n} P[Y_i = y_i \mid {\bf X_i} = {\bf x_i}]
  ', rendering as TeX:
  
                     ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  L(\boldsymbol{{\beta}}) = \prod_{i = 1}^{n} p({\bf x_i})^{y_i} (1 - p({\bf x_i}))^{(1 - y_i)}
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  L(\boldsymbol{{\beta}}) = \prod_{i : y_i = 1}^{n} p({\bf x_i}) \prod_{j : y_j = 0}^{n} (1 - p({\bf x_j}))
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  {\bf x_i}^{\top} \boldsymbol{{\beta}^*} > 0 \implies y_i = 1
  ', rendering as TeX:
  
       ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  {\bf x_i}^{\top} \boldsymbol{{\beta}^*} < 0 \implies y_i = 0
  ', rendering as TeX:
  
       ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\text{E}[Y \mid {\bf X} = {\bf x}]', rendering as TeX:
  ext{E}[Y \mid {\bf X} = {\bf x}]
                     ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\text{E}[Y \mid {\bf X} = {\bf x}] = P[Y = 1 \mid {\bf X} = {\bf x}]', rendering as TeX:
  ext{E}[Y \mid {\bf X} = {\bf x}] = P[Y =
                     ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \begin{aligned}
  \text{E}[Y \mid {\bf X} = {\bf x}] &=  1 \cdot P[Y = 1 \mid {\bf X} = {\bf x}] + 0 \cdot P[Y = 0 \mid {\bf X} = {\bf x}] \\
                                    &= P[Y = 1 \mid {\bf X} = {\bf x}]
  \end{aligned}
  ', rendering as TeX:
  egin{aligned}
                     ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\text{E}[Y \mid {\bf X} = {\bf x}]', rendering as TeX:
  ext{E}[Y \mid {\bf X} = {\bf x}]
                     ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'P[Y = 1 \mid {\bf X} = {\bf x}]', rendering as TeX:
  P[Y = 1 \mid {\bf X} = {\bf x}]
                    ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \log\left(\frac{p({\bf x})}{1 - p({\bf x})}\right) = -2 + 3 x
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \begin{aligned}
  Y_i \mid {\bf X_i} = {\bf x_i} &\sim \text{Bern}(p_i) \\
  p_i &= p({\bf x_i}) = \frac{1}{1 + e^{-\eta({\bf x_i})}} \\
  \eta({\bf x_i}) &= -2 + 3 x_i
  \end{aligned}
  ', rendering as TeX:
  \begin{aligned}
                ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\hat{\eta}({\bf x}) = \log\left(\frac{\hat{p}({\bf x})}{1 - \hat{p}({\bf x})}\right)', rendering as TeX:
  \hat{\eta}({\bf x}) = \log\left(\frac{\h
                  ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\hat{p}({\bf x}) = \frac{e^{\hat{\eta}({\bf x})}}{1 + e^{\hat{\eta}({\bf x})}} = \frac{1}{1 + e^{-\hat{\eta}({\bf x})}}', rendering as TeX:
  \hat{p}({\bf x}) = \frac{e^{\hat{\eta}({
               ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'P[Y = 1 \mid {\bf X} = {\bf x}]', rendering as TeX:
  P[Y = 1 \mid {\bf X} = {\bf x}]
                    ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\hat{\text{E}}[Y \mid {\bf X} = {\bf x}]', rendering as TeX:
  xt{E}}[Y \mid {\bf X} = {\bf x}]
                     ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'P[Y = 1 \mid {\bf X} = {\bf x}]', rendering as TeX:
  P[Y = 1 \mid {\bf X} = {\bf x}]
                    ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \log\left(\frac{\hat{p}({\bf x})}{1 - \hat{p}({\bf x})}\right) = -2.3 + 3.7 x
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\hat{p}({\bf x})', rendering as TeX:
  \hat{p}({\bf x})
               ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \log\left(\frac{p({\bf x})}{1 - p({\bf x})}\right) = 1 + -4 x.
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \begin{aligned}
  Y_i \mid {\bf X_i} = {\bf x_i} &\sim \text{Bern}(p_i) \\
  p_i &= p({\bf x_i}) = \frac{1}{1 + e^{-\eta({\bf x_i})}} \\
  \eta({\bf x_i}) &= 1 + -4 x_i
  \end{aligned}
  ', rendering as TeX:
  \begin{aligned}
                ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\hat{p}({\bf x})', rendering as TeX:
  \hat{p}({\bf x})
               ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \log\left(\frac{p({\bf x})}{1 - p({\bf x})}\right) = -1.5 + 0.5x + x^2.
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \begin{aligned}
  Y_i \mid {\bf X_i} = {\bf x_i} &\sim \text{Bern}(p_i) \\
  p_i &= p({\bf x_i}) = \frac{1}{1 + e^{-\eta({\bf x_i})}} \\
  \eta({\bf x_i}) &= -1.5 + 0.5x_i + x_i^2
  \end{aligned}
  ', rendering as TeX:
  \begin{aligned}
                ^
  unexpected "X"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \eta({\bf x}) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \ldots  + \beta_{p - 1} x_{p - 1}
  ', rendering as TeX:
  
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \log\left(\frac{p({\bf x})}{1 - p({\bf x})}\right) = \beta_0 + \beta_1 x_1 + \ldots  + \beta_{p - 1} x_{p - 1}
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \log\left(\frac{p({\bf x_i})}{1 - p({\bf x_i})}\right) = \beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} + \cdots + \beta_{(p-1)} x_{i(p-1)} + \epsilon_i
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \log\left(\frac{p({\bf x_i})}{1 - p({\bf x_i})}\right) = \beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} + \cdots + \beta_{(q-1)} x_{i(q-1)} + \epsilon_i
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \frac{\hat{\eta}({\bf x}) - \eta({\bf x})}{\text{SE}[\hat{\eta}({\bf x})]} \overset{\text{approx}}{\sim} N(0, 1)
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\eta({\bf x})', rendering as TeX:
  \eta({\bf x})
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \hat{\eta}({\bf x}) \pm z_{\alpha/2} \cdot \text{SE}[\hat{\eta}({\bf x})]
  ', rendering as TeX:
  
                  ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'p({\bf x})', rendering as TeX:
  p({\bf x})
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'p({\bf x})', rendering as TeX:
  p({\bf x})
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \left(\text{logit}^{-1}(\hat{\eta}({\bf x}) - z_{\alpha/2} \cdot \text{SE}[\hat{\eta}({\bf x})] ), \ \text{logit}^{-1}(\hat{\eta}({\bf x}) + z_{\alpha/2} \cdot \text{SE}[\hat{\eta}({\bf x})])\right)
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\hat{\eta}({\bf x})', rendering as TeX:
  \hat{\eta}({\bf x})
                  ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\text{SE}[\hat{\eta}({\bf x})]', rendering as TeX:
  E}[\hat{\eta}({\bf x})]
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\eta({\bf x})', rendering as TeX:
  \eta({\bf x})
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'p({\bf x})', rendering as TeX:
  p({\bf x})
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\eta({\bf x})', rendering as TeX:
  \eta({\bf x})
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math 'p({\bf x})', rendering as TeX:
  p({\bf x})
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\eta({\bf x})', rendering as TeX:
  \eta({\bf x})
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \log\left(\frac{p({\bf x})}{1 - p({\bf x})}\right) = 
  \beta_0 +
  \beta_{1}x_{\texttt{alcohol}} +
  \beta_{2}x_{\texttt{ldl}} +
  \beta_{3}x_{\texttt{famhist}} +
  \beta_{4}x_{\texttt{typea}} +
  \beta_{5}x_{\texttt{age}} +
  \beta_{6}x_{\texttt{ldl}}x_{\texttt{famhist}} +
  \beta_{7}x_{\texttt{ldl}}^2
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  p({\bf x}) = P[Y = 1 \mid {\bf X} = {\bf x}]
  ', rendering as TeX:
  
         ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  1 - p({\bf x}) = P[Y = 0 \mid {\bf X} = {\bf x}].
  ', rendering as TeX:
  
             ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  C^B({\bf x}) = \underset{k}{\mathrm{argmax}} \ P[Y = k \mid {\bf X = x}].
  ', rendering as TeX:
  
           ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \hat{C}(\bf x) = 
  \begin{cases} 
        1 & p({\bf x}) > 0.5 \\
        0 & p({\bf x}) \leq 0.5 
  \end{cases}
  ', rendering as TeX:
  
              ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \hat{C}({\bf x}) = \underset{k}{\mathrm{argmax}} \ \hat{P}[Y = k \mid {\bf X = x}].
  ', rendering as TeX:
  
               ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\hat{p}({\bf x}) = 1 - \hat{p}({\bf x})', rendering as TeX:
  \hat{p}({\bf x}) = 1 - \hat{p}({\bf x})
               ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \hat{C}(\bf x) = 
  \begin{cases} 
        1 & \hat{p}({\bf x}) > 0.5 \\
        0 & \hat{p}({\bf x}) \leq 0.5 
  \end{cases}
  ', rendering as TeX:
  
              ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '\hat{p}({\bf x})', rendering as TeX:
  \hat{p}({\bf x})
               ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \text{Misclass}(\hat{C}, \text{Data}) = \frac{1}{n}\sum_{i = 1}^{n}I(y_i \neq \hat{C}({\bf x_i}))
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  I(y_i \neq \hat{C}({\bf x_i})) = 
  \begin{cases} 
    0 & y_i = \hat{C}({\bf x_i}) \\
    1 & y_i \neq \hat{C}({\bf x_i}) \\
  \end{cases}
  ', rendering as TeX:
  
                     ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \eta({\bf x}) = 0 \iff p({\bf x}) = 0.5
  ', rendering as TeX:
  
            ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace
[WARNING] Could not convert TeX math '
  \hat{C}(\bf x) = 
  \begin{cases} 
        1 & \hat{p}({\bf x}) > c \\
        0 & \hat{p}({\bf x}) \leq c 
  \end{cases}
  ', rendering as TeX:
  
              ^
  unexpected "x"
  expecting "%", "\\label", "\\nonumber" or whitespace

Typos in Logistic chapter

I am reading through the chapter and found some typos/inconsistencies - sorry for not making a pull request (and thanks for making this great book available!)

When introducing the sigmoid function you have

\text{logit}^{-1}(\xi) = \frac{e^\xi}{1 + e^{\xi}} = \frac{1}{1 + e^{-\xi}}

it should be

\text{logit}^{-1}(\xi) = \frac{e^\xi}{1 + e^{\xi}} = \frac{1}{1 + e^{-\xi}}-1

I believe.

Some lines above you have

(Note, many more machine learning focused texts will use p as the number of parameters. This is an arbitrary choice, but you should be aware of it.)

but you are also using p as the number of parameters, so I was confused by the sentence.

Transparency

par(bg = NA)

Also, make plot text grey, to allow for dark and light backgrounds?

Digits

Fix rounding and scientific notation. Remove as much rounding as possible.

Merge MLR Chapter into Book

DD: Proof
DU: Proof
DD: Edit
DD: Merge

Conditioning

Consider notation that makes conditioning explicit.

Instead of doing the download.files() and read.csv() route, how about just embedding the necessary data sets within an R package ala ucidata. From here, the information could downloaded via CRAN or a GH only release.

I think the only data you needed was: autompg?

In the future, these different packages or routines can be made into "virtual" or self-contained STAT 420 package that includes all the relevant material (c.f. msos)

Data Backup

autompg

Checking Independence

Test?
How Sampled?

Graphics needs to be systematized

It would be nice to come up with an indexing scheme for all graphics (figures, plots, tables, etc) so they can be easily and unambiguously referenced from either HTML or PDF text.
For example:
In 7.1.1, after the words"However, its variance remains constant for each xi", there is a following wording to reference a picture with a graph: "This is visually displayed in the image below". I see you guys have fixed it a bit, since I first noticed it, where the picture was actually above the wording, not below. However, still the picture is way down, not even on the same page, but on the next one. It would be better to have a numerical reference, not relative one.

Lines 411 to 414 in cc73a82

    
           ```{r} 
        
           library(broom) 
        
           sim_anova = function(n = 10, mu_a = 0, mu_b = 0, mu_c = 0, mu_d = 0, sigma = 1, stat = TRUE) {

appliedstats/anova.Rmd

Lines 520 to 530 in cc73a82

    
           ```{r} 
        
           get_p_val = function() { 
        
             # create data for two groups, equal mean 
        
             y = rnorm(20, mean = 0, sd = 1) 
        
             g = c(rep("A", 10), rep("B", 10)) 
        
             # p-value of t-test when null is true 
        
             glance(t.test(y ~ g, var.equal = TRUE))$p.value 
        
           }

Maybe save result and manually reload?

```{r sim-anova-function, echo = FALSE}
library(broom)

sim_anova = function(n = 10, mu_a = 0, mu_b = 0, mu_c = 0, mu_d = 0, sigma = 1, stat = TRUE) {
  
  # create data from one-way ANOVA model with four groups of equal size
  # response simulated from normal with group mean, shared variance
  # group variable indicates group A, B, C or D
  sim_data = data.frame(
    response = c(rnorm(n = n, mean = mu_a, sd = sigma),
                 rnorm(n = n, mean = mu_b, sd = sigma),
                 rnorm(n = n, mean = mu_c, sd = sigma),
                 rnorm(n = n, mean = mu_d, sd = sigma)),
    group = c(rep("A", times = n), rep("B", times = n), 
              rep("C", times = n), rep("D", times = n))
  )
  
  # obtain F-statistic and p-value for testing difference of means
  # use lm instead of aov for better result formatting with glance
  aov_results = lm(response ~ group, data = sim_data)
  f_stat = glance(aov_results)$statistic
  p_val  = glance(aov_results)$p.value
  
  # return f_stat if stat = TRUE, otherwise, p-value
  ifelse(stat, f_stat, p_val)
  
}
```

```{r sample-sim-anova-simulation, eval = FALSE}
f_stats = replicate(n = 5000, sim_anova(stat = TRUE))
```


```{r cache-simulation, eval = FALSE, echo = FALSE}
<<sample-sim-anova-simulation>>
saveRDS("cache/f_statistics_simulation.rds", version = 2)
```


```{r load-cached-fstats, echo = FALSE}
f_stats = readRDS("cache/f_statistics_simulation.rds")
```

```{r sim-anova-graphs}
hist(f_stats, breaks = 100, prob = TRUE, border = "dodgerblue", main = "Empirical Distribution of F")
curve(df(x, df1 = 4 - 1, df2 = 40 - 4), col = "darkorange", add = TRUE, lwd = 2)
```

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	```{r}
	sum(x > 3)
	as.numeric(x > 3)
	```

	Here we see that using the `sum()` function on a vector of logical `TRUE` and `FALSE` values that is the result of `x > 3` results in a numeric result. `R` is first automatically coercing the logical to numeric where `TRUE` is `1` and `FALSE` is `0`. This coercion from logical to numeric happens for most mathematical operations.

	```{r}
	library(broom)

	sim_anova = function(n = 10, mu_a = 0, mu_b = 0, mu_c = 0, mu_d = 0, sigma = 1, stat = TRUE) {

	```{r}
	get_p_val = function() {

	# create data for two groups, equal mean
	y = rnorm(20, mean = 0, sd = 1)
	g = c(rep("A", 10), rep("B", 10))

	# p-value of t-test when null is true
	glance(t.test(y ~ g, var.equal = TRUE))$p.value

	}