It is clear from the images that the centre of the box moves horizontally at constant Y 
coordinate.Thus we assume that the box has only one degree of freedom.But once we fix the box ;
theta_1,theta_3,theta_3,theta_4 -the four angles also gets fixed as worked out in 
previous problem(part 3).Thus the system has only one degree of freedom namely : the x co-ordinate.
But the image of the residual variance indeed shows a minima at dimension = 1 but unlike other 
variance images , the variance increases drastically with increasing dimension . But this not an 
error because it is only order of 10^-6 magnitude , so the image if not zoomed flattens out starting 
right from dimension 1 confirming the degrees of freedom.