# What is the significance of the linear phase in the phase response of an M-point moving average filter?

I have plotted the magnitude and the phase responses of an M-point moving average filter, the following are the plots when M = 10:

We can observe that corresponding to every lobe in the magnitude spectrum we have a line in the phase spectrum - a linear phase response is observed corresponding to every lobe. (See the below picture)

I tried to observe the magnitude and phase responses for different values of M and observed a similar pattern.

Is there any reason behind this pattern? Is there any significance for this?

An M-point moving average filter will have a time-delay (for all frequencies) of $$M/2$$, so if you increase the number of points, the phase slope versus frequency will increase.