Question

Prior to removing a parathyroid gland with a disease, two tests are often performed: the standard intact test and the turbo test. These tests work by measuring parathyroid hormone (PTH, in ng/l), but the turbo test is expensive. Researchers obtained data from both tests in a sample of 48 patients to predict turbo test results (y) from standard intact test results (x). The data ranged from roughly 0 to 500 ng/l, and a scatterplot showed a clear linear relationship. The published findings are summarized below:

y = – 4.36 + 1.08x (r = 0.97; n = 48)

For a PTH level of x = 1000 ng/l with the standard intact test, the predicted PTH level with the turbo test is

a) 970 ng/l

b) 148398 ng/l

c) 1036.4 ng/l

d) can't be accurately predicted because it would be extrapolating

Answer 1

given that, y = – 4.36 + 1.08 x

for x=1000,

y hat= 4.36 + (1.08*1000) = 1075.64 ng/ltr.

so,

For a PTH level of x = 1000 ng/l with the standard intact test, the predicted PTH level with the turbo test is:-

d) can't be accurately predicted because it would be extrapolating

in this context,by extrapolation we know that,

Extrapolation is the process of finding a value outside a data set. It could even be said that it helps predict the future! To help us remember what it means, we should think of the part of the word 'extra' as meaning 'more' data than what we originally had.

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