Here are the 5-year temperature averages again.

year = (1955:5:2000)';

y = [ -0.0480; -0.0180; -0.0360; -0.0120; -0.0040;

0.1180; 0.2100; 0.3320; 0.3340; 0.4560 ];

The standard best-fit line results from using a linear polynomial that meets the least squares criterion.

t = year - 1955; % better matrix conditioning later

V = [ t.^0 t ]; % Vandermonde-ish matrix

c = V\y;

f = @(x) polyval(c(end:-1:1),x-1955);

fplot(f,[1955 2000])

hold on, plot(year,y,'.')

xlabel('year'), ylabel('anomaly ({\circ}C)'), axis tight % ignore this line

If we use a global cubic polynomial, the points are fit more closely.

V = [ t.^0 t t.^2 t.^3]; % Vandermonde-ish matrix

c = V\y; f = @(x) polyval(c(end:-1:1),x-1955);

fplot(f,[1955 2000])

If we were to continue increasing the degree of the polynomial, the residual at the data points would get smaller, but overfitting would increase.