Solve, D, and summations
- To: mathgroup at smc.vnet.net
- Subject: [mg64054] Solve, D, and summations
- From: misha <iamisha1 at comcast.net>
- Date: Sun, 29 Jan 2006 05:57:31 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
I am (still) a new user of Mathematica and want to solve for the
(easiest case) least squares estimators.
As usual, I want to choose b_0 and b_1 to minimize S, where S is the sum
of squared differences. i.e.,
In [1]:= S = sum{1,...,n}[y_i - b_0 - (b_1)*x_i]^2
Out [1]= sum{1,...,n}[y_i - b_0 - (b_1)*x_i]^2
After defining this function as above, which gave me the expression as I
expected, I then wrote,
In [2]:= Solve[{D[S, b_0]==0, D[S, b_1]==0}, {b_0, b_1}]
But got
Out [2]= {}
I also tried it this way:
In [3]:= S[b_0, b_1] = sum{1,...,n}[y_i - b_0 - (b_1)*x_i]^2
Out [3]= sum{1,...,n}[y_i - b_0 - (b_1)*x_i]^2
In [4]:= Solve[{D[S, b_0]==0, D[S, b_1]==0}, {b_0, b_1}]
But got
Out [4]= {{}}
Is it the 'n' in the summation that is giving me the problem?
I also tried this:
In [5]:= D[S, b_0]
Out [5]= sum{1,...,n}-2*[y_i - b_0 - (b_1)*x_i]
(as expected)
In [6]:= D[S, b_1]
Out [6]= sum{1,...,n}-2*x_i*[y_i - b_0 - (b_1)*x_i]
After which I copied the returned expressions, set them to zero, and
used Solve as below:
In [7]:= Solve[{sum{1,...,n}-2*[y_i - b_0 - (b_1)*x_i]
==0, sum{1,...,n}-2*x_i*[y_i - b_0 - (b_1)*x_i]==0}, {b_0, b_1}]
But, again, I got
Out [7]= {}
Thank you