I saw a comment by mpiktas that "The sum of two independent t-distributed random variables is not t-distributed". Is it then of any known distribution?
Actually, I am using piece-wise linear regression.
$E(y) = \beta_0 + \beta_1x + \beta_2(x - break)\cdot d$
break = value of predictor x at the breakpoint d = dummy variable = 1, if x > break; 0, otherwise
Effectively, the equation means:
$E(y) = \beta_0 + \beta_1x$
if x > break
$E(y) = (\beta_0 – \beta_2 \cdot break) + (\beta_1+\beta_2)x$
And I want to know whether $x$ is a significant predictor. Couldn't find anything similar on the internet. Thus, I thought of:
- calculating the p-value for $(\beta_1+\beta_2)$ to determine if $x$ is a significant predictor on the right of breakpoint (i.e. when
x > break); and
- using p-value for $\beta_1$ to determine if $x$ is a significant predictor on the left of breakpoint (i.e. when
x =< break).