Time Series 2 Time Series 1 R 2 = 1 Perfectly correlated TS2=5*cos(2*t) TS1=cos(2*t)

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