Magnetic resonance imaging (MRI) is well established as a tool for measuring blood velocities and volume flows. The article "Correlation Analysis of Stenotic Aortic Valve Flow Patterns Using Phase Contrast MRI," referenced in Exercise 1.67, proposed using this methodology for determination of valve area in patients with aortic stenosis. The accompanying data on peak velocity (m/s) from scans of 23 patients in two different planes was read from a graph in the cited paper.

a. Does there appear to be a difference between true average velocity in the two different planes? Carry out an appropriate test of hypotheses (as did the authors of the article).
b. The authors of the article also regressed level-- velocity against level- velocity. The resulting estimated intercept and slope are .14701 and .65393, with corresponding estimated standard errors .07877 and .05947, coefficient of determination .852, and s = .110673. The article included a comment that this regression showed evidence of a strong linear relationship but a regression slope well below 1. Do you agree?

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Level-1.60 .82 .85 .89 .95 1.01 1.01 1.05 Level.50 68 .76 64 68 86 .79 1.03 Level- 1 1.08 1.11 1.18 1.17 1.22 1.29 1.28 1.32 Level75 90 .79 86 99 .80 1.10 1.15 Level- 1 1.37 1.53 1.55 1.85 1.93 1.93 2.14 Level--1 1.04 1.16 1.28 1.39 1.57 1.39 1.32