Chapter 12.4, Problem 54E

The height of a patient is useful for a variety of medical purposes, such as estimating tidal volume of someone in an intensive care who requires artificial ventilation. However, it can be difficult to make an accurate measurement if the patient is confused, unconscious, or sedated. And measurement of height while an individual is lying down is also not straightforward. In contrast, ulna length measurements are generally quick and easy to obtain, even in chair- or bed-bound patients. The accompanying data on x = ulna length (cm) and y = height (cm) for males older than 65 was read from a graph in the article “Ulna Length to Predict Height in English and Portuguese Patient Populations” (European J. of Clinical Nutr., 2012: 209–215).

x	22.5	22.8	22.8	23.3	23.3	24.4	25.0
y	158	155	156	160	161	162	164

x	25.0	25.0	25.0	26.0	26.0	26.8	28.2
y	166	167	170	166	173	178	174

Summary quantities include Σx_i = 346.1, Σy_i = 2310,

S_xx = 36.463571, S_xy = 137.60, S_yy = 626.00.

1. a. Obtain the equation of the estimated regression line and interpret its slope.
2. b. Calculate and interpret the coefficient of determination.
3. c. Carry out a test of model utility.
4. d. Calculate prediction intervals for the heights of two individuals whose ulna lengths are 23 and 25, respectively; use a prediction level of 95% for each interval.
5. e. Based on the predictions of (d), would you agree with the statement in the cited article that “height can be predicted from ulna length with precision”?