Metatarsus adductus (cal it MA) is a turning in of the front part of the foot th

Question

Metatarsus adductus (cal it MA) is a turning in of the front part of the foot that is common in adolescents and usually corrects itself. Hallux abducto valgus (call it HAV) is a deformation of the big toe that is not common in youth and often requires surgery. Perhaps the severity of MA can help predict the severity of HAV. The table below gives data on 38 consecutive patients who came to a medical center for HAV surgery. Using X-rays, doctors measured the angle of deformity for both MA and HAV. They speculated that there is a positive association-more serious MA is associated with more serious HAV Two measurements of foot deformities HAV MA HAV MAHAV MA angle angle angle angle angle angle 25 30 16 17 16 30 12 25 25 15 10 30 10 34 17 21 38 33 23 11 51 12 26 10 14 15 25 25 25 17 13 25 16 28 22 30 26 10 22 18 38 20 28 17 20 10 32 37 13 14 18 15 22 25 20 20 18 21 15 16 10 7 20 10 18 32 12 26 30 19 21 16 31 24 26 16 (a) Translate the question of interest into null and alternative hypotheses. H0: 1 = 0 vs Ha: 1 > 0 Ho: 1 * 0 vs Ha: 1 > 0

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: MV Angle
Independent Variable: HAV Angle
MV Angle = 10.258952 + 0.26447432 HAV Angle
Sample size: 38
R (correlation coefficient) = 0.29402477
R-sq = 0.086450563
Estimate of error standard deviation: 6.5910303

Parameter estimates:

Analysis of variance table for regression model:

Hence,

a) Option B is correct.

b) b1 = 0.2645

t = 1.846

Df = 36

P = 0.0732

Conclusion: Option B is correct.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 10.258952 3.7781637 0 36 2.7153276 0.0101 Slope 0.26447432 0.1432895 0 36 1.8457341 0.0732

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