so I am trying to see whether there is a breakpoint in my data set at a certain time. Basically I have 200 data points and am wondering if there is a breakpoint at t=100, ie whether the slopes of the two regression lines change significantly. Le the slope of line 1= b1 and the slope of line 2= b2.
I want to see whether $b1-b2=0$ using a t test, and so I think that would reduce to evaluating the statistic $t= (b1-b2)/($std error$(b1-b2))$ The problem I have is that I don't know how to compute that standard error since b1 and b2 might be correlated. Furthermore I am not sure what degrees of freedom the corresponding t distribution would have? Finally, how do I even see that the statistic I have written down does follow a t distribution in the first place?
Thanks in advance for anyone who can help me with any of these questions!