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

2. * Time Series 2 Time Series 1 R 2 = 0 No LINEAR correlation TS2=5*cos(2*t) TS1=cos(t)

3. Time Series 1 Time Series 2 R 2 = 0 No correlation TS1=sin(t) TS2=cos(t)

4. Time Series 2 Time Series 1 TS2=cos(t-pi/4) TS1=cos(t)

5. Which linear fit minimizes the error in a least squares sense? A B C Hint, what is the fraction of the variance explained implied by each fit? R 2 = a 1 2 x’ 2 y’ 2

6. Answer C RMS error =.707 implies R 2 =.5RMS error =.767