Generalised linear model with Binomial errors

Question

I have data on germination of acacia seeds. I want to know which germination treatment is better, I am using 6 treatments, one of them being a control. But I got confused about the difference between response and explanatory variable. I have 3 columns Temperature, Germinated seeds and smoke.

Answer 1

Sometimes it can be a little confusing when there are multiple names for the same variable. In an analysis, the response variable is the phenomenon we wish to explain/model. It is also known as the dependent variable, the explained variable, the predicted variable, or the regressand.

Your explanatory variables represent the set of determinants of your response variable, and are otherwise called the independent variable, the control variable, the predictor variable, or the regressor.

In your case, if your sample population consists of the acacia seeds, and you are interested in modelling the probability that a seed will germinate (as the criterion on which you judge treatment quality) using your explanatory variables, you could fit a logistic regression model:

$$\mathrm{logit}(\pi)=\log\left(\frac{\pi}{1-\pi}\right)=\beta_0+\beta X_{1i}+...\beta X_{ki}+\epsilon_i$$

In the above, each explanatory variable is represented by $X$ with a given subscript, modelling the log odds of probability of "success" (germination) as a function of explanatory variables.

The set of estimated coefficients from fitting the logistic regression model can then guide your inference as to which treatment is better.

For more information, here are a good few sources:

https://onlinecourses.science.psu.edu/stat504/node/216

How to interpret logistic regression coefficient

What is the significance of logistic regression coefficients?

Wooldridge, J. M. 2006. Introductory econometrics: a modern approach. Mason, OH, Thomson/South-Western.