1. (15 points) When children are discharged from the hospital their parents may

Question

1. (15 points) When children are discharged from the hospital their parents may still provide substantial care such as the insertion of a feeding tube. It is difficult for parents to know how far to insert the tube, especially with rapidly growing infants. Health care professionals believe it may be possible for parents to measure their child's height and by using a regression equation calculate the appropriate insertion length using a regression equation. At a major children hospital, children and adolescents' heights and esophagus lengths were measured and a regression analysis performed. The data from this analysis is summarized below: Summary statistics from Regression Analysis Height (cm) and Esophageal Length (cm) EsophagusHeight Length (E 34cm 3.5cm 124.5cm 19cm r=0.995, E=11.476 + 0.18111 a. For a child with a height one standard deviation above the mean, what would be the predicted esophagus length? b. What proportion of the variability in esophagus length is accounted for by the height of the children and adolescents? c. From the information presented above, does it appear that the esophagus length can beaccurately predicted from the height of young patients? Provide statistical evidence for your response.

Explanation / Answer

a. Child height one standard above the mean = 124.5 cm + 19 cm = 143.5 cm

Esophageal Length E(143.5cm) = 11.476 + 0.181 H (where H = 37.5 cm)

E = 11.476 + 0.181 * 143.5

E = 37.45 cm

(b) Here r = 0.995

so r2  = 0.99

so, it can be said that 99% of the variability in esophagus length is accounted for the by the height of the children.

(c) As the value of r is pretty hight and near to one. So, it can be said there is very strong linear relationship between the both variables so it appears that the esophagus length can be correctly predicted (99% accurate) from the given linear relationship.

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