# 前言

$$$\begin{split} \mathrm{Var}(\hat{\beta}) & =\mathrm{Var}((X'X)^{-1}X'y)\\ & =(X'X)^{-1}X'\mathrm{Var}(y)((X'X)^{-1}X')'\\ & =(X'X)^{-1}X'\mathrm{Var}(y)X(X'X)^{-1}\\ & =(X'X)^{-1}X'\sigma^{2}IX(X'X)^{-1}\\ & =(X'X)^{-1}\sigma^{2} \end{split} \tag{0.1}$$$

Let $$\mathcal{T}$$ be a topological space, a basis is defined as

$\mathcal{B} = \{B_{\alpha} \in \mathcal{T}\, |\, U = \bigcup B_{\alpha} \forall U \in \mathcal{T} \}$

## 软件信息

xfun::session_info()
## R Under development (unstable) (2019-10-05 r77257)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 8.1 x64 (build 9600)
##
## Locale:
##   LC_COLLATE=Chinese (Simplified)_China.936
##   LC_CTYPE=Chinese (Simplified)_China.936
##   LC_MONETARY=Chinese (Simplified)_China.936
##   LC_NUMERIC=C
##   LC_TIME=Chinese (Simplified)_China.936
##
## Package version:
##   base64enc_0.1.3    BH_1.69.0.1        bookdown_0.14
##   broom_0.5.2        callr_3.3.2        cellranger_1.1.0
##   cli_1.1.0          clipr_0.7.0        codetools_0.2-16
##   colorspace_1.4-1   compiler_4.0.0     crayon_1.3.4
##   curl_4.2           DBI_1.0.0          dbplyr_1.4.2
##   digest_0.6.21      dplyr_0.8.3        ellipsis_0.3.0
##   evaluate_0.14      fansi_0.4.0        forcats_0.4.0
##   fs_1.3.1           generics_0.0.2     ggplot2_3.2.1
##   glue_1.3.1         graphics_4.0.0     grDevices_4.0.0
##   grid_4.0.0         gtable_0.3.0       haven_2.1.1
##   highr_0.8          hms_0.5.1          htmltools_0.4.0
##   httr_1.4.1         jsonlite_1.6       knitr_1.25
##   labeling_0.3       lattice_0.20-38    lazyeval_0.2.2
##   lifecycle_0.1.0    lubridate_1.7.4    magrittr_1.5
##   markdown_1.1       MASS_7.3.51.4      Matrix_1.2.17
##   methods_4.0.0      mgcv_1.8.29        mime_0.7
##   modelr_0.1.5       munsell_0.5.0      nlme_3.1-141
##   openssl_1.4.1      pillar_1.4.2       pkgconfig_2.0.3
##   plogr_0.2.0        plyr_1.8.4         prettyunits_1.0.2
##   processx_3.4.1     progress_1.2.2     ps_1.3.0
##   purrr_0.3.2        R6_2.4.0           RColorBrewer_1.1.2
##   rematch_1.0.1      reprex_0.3.0       reshape2_1.4.3
##   rlang_0.4.0        rmarkdown_1.16     rstudioapi_0.10
##   rvest_0.3.4        scales_1.0.0       selectr_0.4.1
##   splines_3.6.0      stats_4.0.0        stringi_1.4.3
##   stringr_1.4.0      sys_3.3            tibble_2.1.3
##   tidyr_1.0.0        tidyselect_0.2.5   tidyverse_1.2.1
##   tinytex_0.16       tools_4.0.0        utf8_1.1.4
##   utils_4.0.0        vctrs_0.2.0        viridisLite_0.3.0
##   whisker_0.4        withr_2.1.2        xfun_0.10
##   xml2_1.2.2         yaml_2.2.0         zeallot_0.1.0

## 写作环境

### 参考文献

Allaire, JJ, Yihui Xie, Jonathan McPherson, Javier Luraschi, Kevin Ushey, Aron Atkins, Hadley Wickham, Joe Cheng, Winston Chang, and Richard Iannone. 2019. Rmarkdown: Dynamic Documents for R. https://CRAN.R-project.org/package=rmarkdown.

Wickham, Hadley. 2016. ggplot2: Elegant Graphics for Data Analysis. Second. New York, NY: Springer-Verlag. https://doi.org/10.1007/978-3-319-24277-4.

Xie, Yihui. 2015. Dynamic Documents with R and Knitr. 2nd ed. Boca Raton, Florida: Chapman; Hall/CRC. http://yihui.name/knitr/.

Xie, Yihui. 2016. Bookdown: Authoring Books and Technical Documents with R Markdown. Boca Raton, Florida: Chapman; Hall/CRC. https://bookdown.org/yihui/bookdown.

Xie, Yihui, J. J. Allaire, and Garrett Grolemund. 2018. R Markdown: The Definitive Guide. Boca Raton, Florida: Chapman; Hall/CRC. https://bookdown.org/yihui/rmarkdown.