Polynomial fitting prob lem

Hello,
Would anyone have an idea how to prevent these large peaks and troughs occurring at the edges of a polynomial fit?
x = -1:0.005:1;
y = rand(size(x));
polydegree = 15;
coeffs = polyfit(x, y, polydegree);
y = polyval(coeffs,x);
plot(x,y,'k')

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ooh, for instance - is there a way to constrain the polyfit so that the start and end points are always 0?

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