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).

Summary quantities include (xi = 346,1, (yi = 2310, Sxx = 36.463571, Sxy = 137.60, Syy = 626.00.
a. Obtain the equation of the estimated regression line and interpret its slope.
b. Calculate and interpret the coefficient of determination.
c. Carry out a test of model utility.
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.
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"?

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x 22.5 22.8 22.8 23.3 23.3 24.4 25.0 У 158 155 156 160 161 162 164 x25.025.0 25.0 26.0 26.0 26.8 28.2 y 166 67 170 166 173 178 174