Do you want to make *predictions* using your model, or do you want to conduct a *simulation*?

The simple linear regression model is

$$
Y = \beta_0 + \beta_1 X + \varepsilon
$$

and what we estimate is the conditional expected value

$$
E(Y|X) = \beta_0 + \beta_1 X
$$

assuming that $Y|X$ is normally distributed with $\mu = \beta_0 + \beta_1 X$ and some standard deviation $\sigma$.

If you want to make **predictions** from your model, then given new value $x^*$ as your prediction for $y^*$ you take

$$
y^* = \hat\beta_0 + \hat\beta_1 x^*
$$

so you predict what you were estimating, i.e. the conditional mean. 

On another hand, if you want to **simulate** data according to your model, then you would draw samples from the normal distribution

$$
y_\text{sim} \sim \mathcal{N}(\hat\beta_0 + \hat\beta_1 x^*, \, \sigma)
$$

As image is worth thousand words, the following plot shows predictions from the linear regression model (red dots) against the data that was used to estimate the model (blue dots) and the values simulated according to the the model (gray dots).

[![Regression: data vs fitted values vs simulated values][1]][1]


  [1]: https://i.sstatic.net/JDdCY.png