MS part 3b) Results - model equation

Vignette Author

2018-12-10

Introduction

Zuur and Ieno (2016) encourage authors to present the model equation associated with their analyses (“Step 5: Present the statistical model”). This is a very important aspect of an analysis but requires you to know how to interpret R’s output and to understand what the underlying relationships which your “Statistical test” implies.

Zuur & Ieno (2016) provide some examples, but they are for fairly complex models. I am working on simpler examples.

Here are some thoughts on understanding and implementing this task

Simple regression: use ggpubr!

For simple regression situations we can get ggpubr to come up with the equation for us.

Some packages and data

library(ggpubr)
library(MASS)
data(mammals)

A simple regression model

mod <- lm(brain ~ body, data = mammals)

Look at the output

summary(mod)
#> 
#> Call:
#> lm(formula = brain ~ body, data = mammals)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -810.07  -88.52  -79.64  -13.02 2050.33 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) 91.00440   43.55258    2.09   0.0409 *  
#> body         0.96650    0.04766   20.28   <2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 334.7 on 60 degrees of freedom
#> Multiple R-squared:  0.8727, Adjusted R-squared:  0.8705 
#> F-statistic: 411.2 on 1 and 60 DF,  p-value: < 2.2e-16

The intercept is 91 and the slope is 0.97

This is an equation for

brain ~ body brain ~ intercept + slopebody brain ~ 91 + 0.97body

ggscatter(data = mammals,
       y = "brain",
       x = "body", 
       add = "reg.line") +
  stat_regline_equation()

References on regession and regression equations

For general information on how to interpret regression equations see these papers

Boldina & Beninger. 2016. Strengthening statistical usage in marine ecology: Linear regression. Journal of Experimental Marine Biology & Ecology

Marril. 2004. Advanced Statistics: Linear Regression, Part I: Simple Linear Regression. Emergency Medicine

Marril 2008. Advanced Statistics: Linear Regression, Part II: Multiple Linear Regression. Emergency Medicine

Schneider et al 2010. Linear regression analysis: part 14 of a series on evaluation of scientific publications. Deutsches Ärzteblatt.

Zuur & Ieno. 2016. A protocol for conducting and presenting results of regression‐type analyses https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/2041-210X.12577