Sports scientists want to use nuclear magnetic resonance spectroscopy, NMR, to predict the muscle fibre composition in the thighs of athletes. They obtained the data in the screenshot, which contains three variables: FTF – the percentage of fast twitch fibres in the muscle. T1 – the T1 relaxation time measured in ms. T2 – the T2 relaxation time measured in ms. (a) Perform a linear regression to determine the equation allowing FTF to be predicted by T1, i.e. FTF = b0 + b­1T1. i) What is the equation of the best-fit line? ii) What is the F statistic and P value for the regression? Do these indicate that the regression is significant? iii) What is the value of R2? How much variation does the regression take account of?

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Sports scientists want to use nuclear magnetic resonance spectroscopy, NMR, to predict the muscle fibre composition in the thighs of athletes. They obtained the data in the screenshot, which contains three variables:

  • FTF – the percentage of fast twitch fibres in the muscle.
  • T1 – the T1 relaxation time measured in ms.
  • T2 – the T2 relaxation time measured in ms.

(a) Perform a linear regression to determine the equation allowing FTF to be predicted by T1, i.e. FTF = b0 + b­1T1.

i) What is the equation of the best-fit line?

ii) What is the F statistic and P value for the regression? Do these indicate that the regression is significant?

iii) What is the value of R2? How much variation does the regression take account of?

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
FTF
38
44
39
33
29
45
47
55
58
55
61
67
68
69
72
93
T1
313
320
322
320
321
324
332
348
350
354
362
364
368
373
382
379
tutulub
T2
22.3
26.7
25.6
24.5
23.0
28.1
26.5
28.3
28.3
31.0
29.5
29.7
29.9
30.0
32.3
32.7
var
var
var
var
var
Transcribed Image Text:1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 FTF 38 44 39 33 29 45 47 55 58 55 61 67 68 69 72 93 T1 313 320 322 320 321 324 332 348 350 354 362 364 368 373 382 379 tutulub T2 22.3 26.7 25.6 24.5 23.0 28.1 26.5 28.3 28.3 31.0 29.5 29.7 29.9 30.0 32.3 32.7 var var var var var
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