Data babies in openintro package

## Rows: 1,236
## Columns: 8
## $ case      <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1…
## $ 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, 2…
## $ 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, 1…
## $ smoke     <int> 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, …

Notation

$y_i={\beta }_0+{\beta }_1{x}_{1i}+{\beta }_2{x}_{2i}+{ϵ}_i$

${\beta }_0$ is intercept
${\beta }_1$ is the slope for gestation
${\beta }_2$ is the slope for smoke ${ϵ}_i$ is error/residual
$i=1,2,...n$ identifier for each point

model_gs <- lm(bwt ~ gestation + smoke, data = babies)
tidy(model_gs)

## # A tibble: 3 x 5
##   term        estimate std.error statistic  p.value
##   <chr>          <dbl>     <dbl>     <dbl>    <dbl>
## 1 (Intercept)   -0.932    8.15      -0.114 9.09e- 1
## 2 gestation      0.443    0.0290    15.3   3.16e-48
## 3 smoke         -8.09     0.953     -8.49  5.96e-17

Expected birth weight for a baby who had 280 days of gestation with a smoker mother

$\widehat{{\text{bwt}}_i}=b_0+b_1{\text{gestation}}_i+b_2{\text{smoke}}_i$

$\widehat{{\text{bwt}}_i}=-0.932+(0.443\times 280)+(-8.09\times 1)$

babies %>% 
  modelr::add_predictions(model_gs) %>% 
  select(bwt, gestation, smoke, pred)

## # A tibble: 1,236 x 4
##      bwt gestation smoke  pred
##    <int>     <int> <int> <dbl>
##  1   120       284     0  125.
##  2   113       282     0  124.
##  3   128       279     1  115.
##  4   123        NA     0   NA 
##  5   108       282     1  116.
##  6   136       286     0  126.
##  7   138       244     0  107.
##  8   132       245     0  108.
##  9   120       289     0  127.
## 10   143       299     1  123.
## # … with 1,226 more rows

babies %>% 
  modelr::add_predictions(model_gs) %>% 
  modelr::add_residuals(model_gs) %>% 
  select(bwt, gestation, smoke, pred, resid)

## # A tibble: 1,236 x 5
##      bwt gestation smoke  pred  resid
##    <int>     <int> <int> <dbl>  <dbl>
##  1   120       284     0  125.  -4.84
##  2   113       282     0  124. -11.0 
##  3   128       279     1  115.  13.5 
##  4   123        NA     0   NA   NA   
##  5   108       282     1  116.  -7.87
##  6   136       286     0  126.  10.3 
##  7   138       244     0  107.  30.9 
##  8   132       245     0  108.  24.4 
##  9   120       289     0  127.  -7.05
## 10   143       299     1  123.  19.6 
## # … with 1,226 more rows