Last updated: 2020-05-27

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This summarizes key concepts and directions for performing linear regression. Most of the steps are taken from Duke University’s Linear Regression and Modeling course on coursera.


Linear Regression

1. Correlation

  • correlation is the strength of linear association

  • correlation coefficients are sensitive to outliers

  • R = cor(x,y). R-squared = (correlation)^2.

This is the correlation code for a table (x=temp, y=sound).

cor <- cricket %>% 
  summarise(r=cor(sound, temp)) %>% 
  pull(r)
cor
[1] 0.8351438

This is the scatterplot to see the points.

ggplot(cricket, aes(x=temp, y=sound))+
  geom_point(alpha=0.5)+
  geom_smooth(method = "lm", se=F)

2. Residuals

Residuals are the difference between observed and predicted values. To visualize this we have used the broom package to test the residuals.

  • Residuals (errors) = observed - predicted
lm <- lm(sound~temp, data=cricket)
lm.table <- augment(lm) #can visualize all the residuals in a table form

ggplot(lm.table, aes(x=.fitted, y=.resid))+ geom_point(alpha=0.5)

3. Least Square Lines



sessionInfo()
R version 4.0.0 (2020-04-24)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Catalina 10.15.4

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] broom_0.5.6     readxl_1.3.1    forcats_0.5.0   stringr_1.4.0  
 [5] dplyr_0.8.5     purrr_0.3.4     readr_1.3.1     tidyr_1.0.3    
 [9] tibble_3.0.1    ggplot2_3.3.0   tidyverse_1.3.0 workflowr_1.6.2

loaded via a namespace (and not attached):
 [1] tidyselect_1.1.0 xfun_0.13        splines_4.0.0    haven_2.2.0     
 [5] lattice_0.20-41  colorspace_1.4-1 vctrs_0.3.0      generics_0.0.2  
 [9] htmltools_0.4.0  mgcv_1.8-31      yaml_2.2.1       rlang_0.4.6     
[13] later_1.0.0      pillar_1.4.4     withr_2.2.0      glue_1.4.1      
[17] DBI_1.1.0        dbplyr_1.4.3     modelr_0.1.7     lifecycle_0.2.0 
[21] munsell_0.5.0    gtable_0.3.0     cellranger_1.1.0 rvest_0.3.5     
[25] evaluate_0.14    labeling_0.3     knitr_1.28       httpuv_1.5.2    
[29] fansi_0.4.1      Rcpp_1.0.4.6     promises_1.1.0   backports_1.1.6 
[33] scales_1.1.1     jsonlite_1.6.1   farver_2.0.3     fs_1.4.1        
[37] hms_0.5.3        digest_0.6.25    stringi_1.4.6    grid_4.0.0      
[41] rprojroot_1.3-2  cli_2.0.2        tools_4.0.0      magrittr_1.5    
[45] crayon_1.3.4     pkgconfig_2.0.3  Matrix_1.2-18    ellipsis_0.3.0  
[49] xml2_1.3.2       reprex_0.3.0     lubridate_1.7.8  rstudioapi_0.11 
[53] assertthat_0.2.1 rmarkdown_2.1    httr_1.4.1       R6_2.4.1        
[57] nlme_3.1-147     git2r_0.27.1     compiler_4.0.0