Why don't the Inner matrix dimensions agree when adding an extra variable?

Tim Bennett

2012 11 22

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I'm using multiple regression to obtain the coefficients from 3 predictor variables (x1, x2, x3, each a [1 x 20] array) and two outcome variables (x and y, each a [1 x 20] array). Using the following code:

X = [ones(length(x1),1) x1' x2' x3'];

B = X\devY';

B(1,:)=[]

J = B';

Z = null(J);

to import the [4 x 2] coefficients into a [2 x 3] Jacobian matrix (J) (removing the constant values) from which the null(J)is used to calculate an output known as the UCM using the following code:

for i = 1:N

UCM(:,i) = (Z'*dev(:,i))*Z;

end

This code works for 3 predictor and 2 output variables. However if I add an extra predictor variable (x4) (a [1 x 20] array) I get the following warning:

Error using ==> mtimes Inner matrix dimensions must agree.

Any help would be appreciated.

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Tim Bennett 2012-11-22

编辑：Tim Bennett 2012-11-22

Z is a [3 x 1] array and dev is a [3 x 20] array (i.e. the deviations of three performance variables combined: x1, x2, and x3] using the following code:

[M,N] = size(data);

mn = mean(data,2);

dev = data-repmat(mn,1,N);

x1 = dev (1,:);

x2 = dev (2,:);

x3 = dev (3,:);

Tim Bennett 2012-11-25

编辑：Tim Bennett 2012-11-25

Hi guys,

if you're not already tired of my questions I have a bit more information to hopefully make a bit more sense. Any help would be appreciated.

I'm trying to see how joint angles of the right leg (predictor variables, X = x1, x2, x3 for the hip, knee, and ankle angles respectively each a [1 x 20] array) could potentially stablise the position of the right foot (outcome variables Y = x,y coordinate positions: both a [1 x 20] array) using linear regression.

"dev" (a [1 x 20] array for each predictor variable) is the deviations of joint angles from the mean joint angle configuration at each trial and projected onto the null-space or null(J)(Z = null(J)) using the following code:

for i = 1:N

UCM(:,i) = (Z'*dev(:,i))*Z;

end

The UCM is used to look at the control of a movement and is approximated linearly using the null space (Z) of the J matrix.

This code works for one frame (i.e. a [1 x 20] array) and a whole normalised movement cycle (i.e. a [101 x 20] array) for 3 predictor varibles (PV's) and 2 output variables (OV's) from a [3 x 1] Z array.

However when I increase the number of PV's to 4 (resulting in a [4 x 2] Z array) and 5 (resulting in a [5 x 2] Z array) with 2OV's, I get the following warning:

???Error using mm>mtimes

Inner matrix dimensions must agree

Therefore, i'm unable to analyse any data above three PV's. Can you help indentify where i'm going wrong?

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