2 Simple Linear Regression - Example: Cancer Experiment

2.1 Background

2.1.1 Required Packages

library(tidyverse)    # Loads several very helpful 'tidy' packages
library(haven)        # Read in SPSS datasets
library(psych)        # Lots of nice tid-bits
library(GGally)       # Extension to 'ggplot2' (ggpairs)

2.1.2 Example Dataset - Cancer Experiment

The Cancer dataset:

cancer_raw <- haven::read_spss("https://raw.githubusercontent.com/CEHS-research/eBook_ANOVA/master/data/Cancer.sav")

tibble::glimpse(cancer_raw)

Observations: 25
Variables: 9
$ ID       <dbl> 1, 5, 6, 9, 11, 15, 21, 26, 31, 35, 39, 41, 45, 2, 12...
$ TRT      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1,...
$ AGE      <dbl> 52, 77, 60, 61, 59, 69, 67, 56, 61, 51, 46, 65, 67, 4...
$ WEIGHIN  <dbl> 124.0, 160.0, 136.5, 179.6, 175.8, 167.6, 186.0, 158....
$ STAGE    <dbl> 2, 1, 4, 1, 2, 1, 1, 3, 1, 1, 4, 1, 1, 2, 4, 1, 2, 1,...
$ TOTALCIN <dbl> 6, 9, 7, 6, 6, 6, 6, 6, 6, 6, 7, 6, 8, 7, 6, 4, 6, 6,...
$ TOTALCW2 <dbl> 6, 6, 9, 7, 7, 6, 11, 11, 9, 4, 8, 6, 8, 16, 10, 6, 1...
$ TOTALCW4 <dbl> 6, 10, 17, 9, 16, 6, 11, 15, 6, 8, 11, 9, 9, 9, 11, 8...
$ TOTALCW6 <dbl> 7, 9, 19, 3, 13, 11, 10, 15, 8, 7, 11, 6, 10, 10, 9, ...

cancer_clean <- cancer_raw %>% 
  dplyr::rename_all(tolower) %>% 
  dplyr::mutate(id = factor(id)) %>% 
  dplyr::mutate(trt = factor(trt,
                             labels = c("Placebo", 
                                        "Aloe Juice"))) %>% 
  dplyr::mutate(stage = factor(stage))

tibble::glimpse(cancer_clean)

Observations: 25
Variables: 9
$ id       <fct> 1, 5, 6, 9, 11, 15, 21, 26, 31, 35, 39, 41, 45, 2, 12...
$ trt      <fct> Placebo, Placebo, Placebo, Placebo, Placebo, Placebo,...
$ age      <dbl> 52, 77, 60, 61, 59, 69, 67, 56, 61, 51, 46, 65, 67, 4...
$ weighin  <dbl> 124.0, 160.0, 136.5, 179.6, 175.8, 167.6, 186.0, 158....
$ stage    <fct> 2, 1, 4, 1, 2, 1, 1, 3, 1, 1, 4, 1, 1, 2, 4, 1, 2, 1,...
$ totalcin <dbl> 6, 9, 7, 6, 6, 6, 6, 6, 6, 6, 7, 6, 8, 7, 6, 4, 6, 6,...
$ totalcw2 <dbl> 6, 6, 9, 7, 7, 6, 11, 11, 9, 4, 8, 6, 8, 16, 10, 6, 1...
$ totalcw4 <dbl> 6, 10, 17, 9, 16, 6, 11, 15, 6, 8, 11, 9, 9, 9, 11, 8...
$ totalcw6 <dbl> 7, 9, 19, 3, 13, 11, 10, 15, 8, 7, 11, 6, 10, 10, 9, ...

psych::headTail(cancer_clean)

# A tibble: 9 x 9
  id    trt        age   weighin stage totalcin totalcw2 totalcw4 totalcw6
  <fct> <fct>      <chr> <chr>   <fct> <chr>    <chr>    <chr>    <chr>   
1 1     Placebo    52    124     2     6        6        6        7       
2 5     Placebo    77    160     1     9        6        10       9       
3 6     Placebo    60    136.5   4     7        9        17       19      
4 9     Placebo    61    179.6   1     6        7        9        3       
5 <NA>  <NA>       ...   ...     <NA>  ...      ...      ...      ...     
6 42    Aloe Juice 73    181.5   0     8        11       16       <NA>    
7 44    Aloe Juice 67    187     1     5        7        7        7       
8 50    Aloe Juice 60    164     2     6        8        16       <NA>    
9 58    Aloe Juice 54    172.8   4     7        8        10       8       

2.2 Exploratory Data Analysis: i.e. the eyeball method

2.2.1 Scatterplot

Always plot your data first!

cancer_clean %>% 
  ggplot(aes(x = age,
             y = weighin)) +
  geom_point() +
  geom_smooth(method = "lm",    se = TRUE,  color = "blue") +  # straight line (linear model)
  geom_smooth(method = "loess", se = FALSE, color = "red")     # loess line (moving window)