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The model is:

$Y_i = B_i + B_2x_i + e_i$ $i= 1, ... , 10$

$x_i = i$

$y = (8,4,4,7,8,8,4,9,4,5)$

I'm find:

$[B_1, B_2]^T = [84.77; 13.67]^T$

$s^2 = 5.20$

On the same data, adapt the following model:

$Y_i = a + e_i$
$x_i < 6 $

$Y_i = a + b(x_i-1)$
$x_i >= 6$

I must find the estimate of maximum likelihood of $B* = (a,b)^t$ of the new model $Y = X*B*$

I'm trying to solve the system but...I can't find a solution...

  1. $B_i + B_2x_i = a $

  2. $B_i + B_2x_i = a + b(x_i-1)$

  3. $B_i + B_2x_i = a $

  4. $B_i + B_2x_i = a + bx_i-b$

I don't think, I should recalculate everything from the beginning....It seems strange and anyway I already have the values ​​of B estimators... Any ideas?

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  • $\begingroup$ Hint: the new model replaces $x=(1,2,\ldots,10)$ by $(0,0,0,0,0,5,6,7,8,9)$. $\endgroup$
    – whuber ♦
    Commented Jul 7, 2017 at 21:31
  • $\begingroup$ Did you solve the equation system ? $\endgroup$
    – Valentina
    Commented Jul 8, 2017 at 6:52

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