As explained in [this course handout (page 1)](https://www.zoology.ubc.ca/~bio501/lecturepdf/07.Glm.pdf), a linear model can be written in the form:

$$ y = \beta\_1 x\_{1} + \cdots + \beta\_p x\_{p} + \varepsilon\_i,$$

where $y$ is the response variable and $x\_{i}$ is the $i^{th}$ explanatory variable.

Often with the goal of meeting test assumptions, one can transform the response variable. For example we apply the log function on each $y\_i$. Transforming a response variable does NOT equate to doing a GLM.

A GLM can be written in the following form (from the [course handout again (page 3)](https://www.zoology.ubc.ca/~bio501/lecturepdf/07.Glm.pdf))

$$ g(u) = \beta\_1 x\_{1} + \cdots + \beta\_p x\_{p} + \varepsilon\_i,$$

where $u$ is just another symbol for $y$ as I understand from page 2 in the course handout. $g()$ is called the link function.

I don't really understand the difference between a GLM and LM with transformed variable from the slides in the course. Can you help me with that?