In charlotte-ngs/asmss2022: Applied Statistical Methods in Animal Science - Spring Semester 2022

knitr::opts_chunk$set(echo = TRUE)

# define data directory depending on online status
if (params$isonline){
  s_data_dir <- "https://charlotte-ngs.github.io/asmss2022/data"
} else {
  s_data_dir <- file.path(here::here(), "docs", "data")
}
s_data_path <- file.path(s_data_dir, "asm_bw_mult_reg.csv")
s_data_bw_bc_path <- file.path(s_data_dir, "asm_bw_bc_reg.csv")
# write the default one variable regression, if we are not online
if (!params$isonline){
  tbl_mult <- readr::read_csv(file = s_data_path)
  tbl_bw_bc <- dplyr::select(tbl_mult, Animal, `Breast Circumference`, `Body Weight`)
  if (!fs::file_exists(path = s_data_bw_bc_path))
    readr::write_csv(tbl_bw_bc, file = s_data_bw_bc_path)
}
tbl_bw_bc <- readr::read_csv(file = s_data_bw_bc_path)
n_nr_obs <- nrow(tbl_bw_bc)

Problem 1: Measurement Unit

The measurement unit has an influence on the results of a regression model. This is demonstrated by changing the unit for Breast Circumference (BC) from centimeters to meters.

Tasks

• Read the original dataset with BC and BW for r n_nr_obs animals. The dataset is availble as csv-file under: r s_data_bw_bc_path
• Convert all values of BC from centimeters to meters
• Run the regression model using lm()
• Compare the results with the results from the original model

Solution

• Use the function readr::read_csv() to read the data

s_data_bw_bc_url <- "https://charlotte-ngs.github.io/asmss2022/data/asm_bw_bc_reg.csv"
tbl_bw_bc <- readr::read_csv(file = s_data_bw_bc_path)

• Divide all values in column Breast Circumference by 100

tbl_bw_bc$`Breast Circumference` <- tbl_bw_bc$`Breast Circumference` / 100

• Run the regression using lm()

lm_bw_bc_m <- lm(formula = `Body Weight` ~ `Breast Circumference`, data = tbl_bw_bc)
summary(lm_bw_bc_m)

• Comparison of results: intercept is the same, because it has the same unit as the response variable Body Weight. The regression slope is multiplied by 100 compared to the result of the original dataset where Breast Circumference is in cm.

• Although according to the International System of Units (https://en.wikipedia.org/wiki/International_System_of_Units) meter is the official unit for length, it does not make sense to use meter as unit for breast circumference. This is because the range of measurement for breast circumference is very narrow when the values are expressed in meters. Furthermore the increment of $1$ meter is very unrealistic, compared to the range of available measurement value for breast circumference.

Problem 2: Significance Level

Do the same type of comparison of regression modelling results when changing the measurement unit for the variable HEI in the complete dataset given in

https://charlotte-ngs.github.io/asmss2022/data/asm_bw_mult_reg.csv.

Tasks

• Run the same regression model as in Problem 1 of Exercise 1
• Convert the measurement unit for the variable HEI from centimeter to meter
• Compare the results of the two regression models with a special focus on the significance level

Solution

• Start by reading the data

s_sol02_p02_path <- "https://charlotte-ngs.github.io/asmss2022/data/asm_bw_mult_reg.csv"
tbl_sol02_p02 <- readr::read_csv(file = s_sol02_p02_path)

• Regression model

lm_sol02_p02 <- lm(formula = `Body Weight` ~ `Breast Circumference` + BCS + HEI, 
                   data = tbl_sol02_p02)
summary(lm_sol02_p02)

• Convert HEI to meters

tbl_sol02_p02_HEI_in_m <- tbl_sol02_p02
tbl_sol02_p02_HEI_in_m$HEI <- tbl_sol02_p02_HEI_in_m$HEI / 100

• Run the regression model with the new data

lm_sol02_p02_HEI_in_m <- lm(formula = `Body Weight` ~ `Breast Circumference` + BCS + HEI, 
                            data = tbl_sol02_p02_HEI_in_m)
summary(lm_sol02_p02_HEI_in_m)

• Comparison of results: As already seen in Problem 1, the regression coefficients change by a factor of $100$. But because also the standard error are $100$ times bigger in the second regression model, the significance result does not change.

charlotte-ngs/asmss2022 documentation built on June 7, 2022, 1:33 p.m.