How to obtain the a and b coefficient of a trend equation Y(t)=a+b*t from a set of time series data?

Y = [375.2 414.2 458.5 511.9 542 588.1 656.4 722.5 804.2 896.8 957.4 1038.7 1069.3 1167.9 1281.7 1365.8]
t = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]
X =[710 771.8 834.8 943.8 1033.7 1138.4 1248.8 1375.3 1546.5 1724.6 1914.3 2121.8 2255.1 2424.9 2662.1 2832.1]

Assume

Trend equation for data X
Linear Y(t) = a +b*t
Quadratic  Y(t) = a +b*t+c*t^2
Cubic       Y(t) = a +b*t+c*t^2+d*t^3
Causal equation
Linear Y(x)=r+s*X(t)

In SPSS, the data mining software clementine can easily sort out the coef of a b c d r and s of the above equations from the above data.

Please advise how to do it in MATLAB using statistical tools.

Lucas Lai

Answer 1

[Matt J]

Use polyfit().