Plot function generates markers but not lines

This is a least-squares problem, but I cannot get the "best fit line" to generate. I can plot markers however. Specifying '-', 'LineWidth' and others do not work. What am I doing wrong here? Software is R2015a

WS = [1912 82.2; 1920 73.6; 1924 72.4; 1928 71; 1932 66.8; 1936 65.9;
    1948 66.3; 1952 68.8; 1956 62; 1960 61.2; 1964 59.5; 1968 60;
    1972 58.59; 1976 55.65; 1980 54.79; 1984 55.92; 1988 54.93; 1992 54.65;
    1996 54.50; 2000 53.83; 2004 53.84; 2008 53.12; 2012 53.00];
A = zeros(23,2); %shapes matrix dimensions for dataset
A(1:23,1) = ones; %design matrix ones

A(1:23,2) = WS(1:23,1); %fills design matrix with the independent variables
b = WS(1:23,2); %allocates parameters from dataset

x = (inv(A' * A)) * (A') * b;

for k = 1:23

      y = (x(1,1) + x(2,1) * A(k,2));

      plot(A(k,2),y)

      hold on;

end

Answer 1

[dpb]

Wrong way to go about it...using the explicit design matrix and direct inversion is poor numerically...instead

plot(WS(:,1), WS(:,2))             % plot raw data
coef=polyfit(WS(:,1), WS(:,2),1);  % Linear LS polynomial
yHat=polyval(coef,WS(:,1));        % compute fitted values
hold on
plot(WS(:,1), yHat,'r-')           % add predicted values

The reason your plot only produces markers is you're plotting a single point at a time in the loop instead of drawing the line with the vectors.

See

doc polyfit % and friends

or for more general models than polynomial,

doc \ % or "mldivide"

for the generalized matrix "left divide" implemented in Matlab that is much more robust numerically.

[K G]

Thank you for this. Unfortunately, after inquiring with my professor, we can't use the polyfit function. This is a linear algebra course and the lab component is designed to be marked according to what or how we learn MatLab. I know my code is cumbersome, but do you have any other ideas?

[dpb]

Well, the code "works" in solving but I'd iterate the caveat re: the numerics in general. Perhaps your course will cover that later.

I would, however, even if using the explicit formulation, modify the naming convention you've chosen to return the solution for the coefficients in a variable that has some relation to what it is.

The problem you're having with the plotting is as outlined; you're plotting each point individually; even if you use the technique you have to solve for the coefficients you can still compute the results with a vector expression then plot the results without a loop.

As it is class work, I'll let the hint suffice for now... :)

[Walter Roberson]

Replace your

y = (x(1,1) + x(2,1) * A(k,2));

with

y(k) = (x(1,1) + x(2,1) * A(k,2));

and delete the plot() you have there. Then after the loop,

plot(A(2,:), y)