class: center, middle, inverse, title-slide # Binary Predictors ### Dr. Dogucu --- layout: true <div class="my-header"></div> <div class="my-footer"> Copyright &copy; <a href="https://mdogucu.ics.uci.edu">Dr. Mine Dogucu</a>. <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a></div> --- #### Data `babies` ``` ## Rows: 1,236 ## Columns: 8 ## $ case <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, … ## $ bwt <int> 120, 113, 128, 123, 108, 136, 138, 132, 120, 143, 140, 144,… ## $ gestation <int> 284, 282, 279, NA, 282, 286, 244, 245, 289, 299, 351, 282, … ## $ parity <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,… ## $ age <int> 27, 33, 28, 36, 23, 25, 33, 23, 25, 30, 27, 32, 23, 36, 30,… ## $ height <int> 62, 64, 64, 69, 67, 62, 62, 65, 62, 66, 68, 64, 63, 61, 63,… ## $ weight <int> 100, 135, 115, 190, 125, 93, 178, 140, 125, 136, 120, 124, … ## $ smoke <int> 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1,… ``` --- class: middle <div align = "center"> | y | Response | Birth weight | Numeric | |---|-------------|-----------------|---------| | x | Explanatory | Smoke | Binary | --- class: middle center `$$bwt_i = \beta_0 + \beta_1smoke_i +\epsilon_i$$` -- `$$\hat {bwt_i} = \beta_0 + \beta_1smoke_i$$` --- ```r model_s <- lm(bwt ~ smoke, data = babies) tidy(model_s) ``` ``` ## # A tibble: 2 x 5 ## term estimate std.error statistic p.value ## <chr> <dbl> <dbl> <dbl> <dbl> ## 1 (Intercept) 123. 0.649 190. 0. ## 2 smoke -8.94 1.03 -8.65 1.55e-17 ``` -- .pull-left[ **Non-smoker mother** `\(\hat bwt_i = 123 - 8.94\times 0\)` `\(\hat bwt_i =123\)` ] .pull-right[ **Smoker mother** `\(\hat bwt_i = 123 - 8.94\times 1\)` `\(\hat bwt_i =114.06\)` ] -- The slope represents the difference between two groups. The difference is significant.