I am not sure about this plot if it looks good as the dots appear around the line. So I just want to ask if it looks okay. My data is quite large (almost 3000 observations) and maybe that is why it looks like this.

I am not sure about this plot if it looks good as the dots appear around the line. So I just want to ask if it looks okay. My data is quite large (almost 3000 observations) and maybe that is why it looks like this.

Have you tried plotting this using ggplot2 in R? It has a nice semi transparency feature with the Cairo package which makes guesstimating the mean for such residual plots easy. For example you could have each point semi transparent and you could visually check if they are centered around 0. But overall by looking at the image you posted, no reason to think otherwise.
The plot of the residual looks good. To be very sure get the mean it should be very close to zero. In fact it should approximate to zero when you approximate to 1 decimal place