Notice that the $\hat{f}$ don't have an error term, $\epsilon$, as would be expected for regression models. Why don't these models have an error term? I am currently reading some notes on linear and polynomial regression. The notes say the following:

The linear model is
$$\hat{f}_L (X) = \beta_0 + \beta_1 X$$
The quadratic model is
$$\hat{f}_Q(X) = \beta_0 + \beta_1 X + \beta_2 X^2$$

Notice that the $\hat{f}$ don't have an error term, $\epsilon$, as would be expected for regression models. Why don't these models have an error term?

Have a look at wikipedia
The hat on top of a variable (e.g. $\hat{f}_L(X)$) typically indicates that the variable is an estimator of some observable. Namely, it is a function of a sample from a random variable, which can be used to estimate something of real world relevance, such as Celsius temperature given Farenheit temperature measurement. This view is derived from a more general view concerning relationships of random variables themselves. There, as you see in wiki first equation, the errors are present. I would say that it is more precise to call what you have above a linear estimator and not a linear model, but I am not the author of the book you are reading
