Time Series 2Time Series 1
R2 = 1Perfectly correlated
TS2=5*cos(2*t)TS1=cos(2*t)
*Time Series 2Time Series 1
R2 = 0No LINEAR correlation
TS2=5*cos(2*t)TS1=cos(t)
Time Series 1Time Series 2
R2 = 0No correlation
TS1=sin(t)TS2=cos(t)
Time Series 2Time Series 1
TS2=cos(t-pi/4)TS1=cos(t)
Which linear fit minimizes the error in a least squares sense?
AB
C
Hint, what is the fractionof the variance explainedimplied by each fit?
R2= a12 x’2
y’2
Answer C
RMS error = .707 implies R2=.5 RMS error = .767