Question

A researcher investigated the anatomical and pathological status of the corticospinal tracts,
somatosensory tracts, and parietal lobes of patients who had had cerebral palsy and mental retardation.
As a part of the study, measurements were taken on the parietal lobes and medullary pyramid areas of
the subjects’ brains.
The results for six spastic subjects are shown in Table 1 below.
Table 1: Patients lobe weights and pyramidal areas of six spastic subjects
Parietal lobe weight, g (Y): 162 123 121 127 154 150
Pyramidal area, mm 2 (X): 10.2 8.2 7.8 7.6 9.9 9.3
(maximum 200 words)
a) Plot a scatter diagram for parietal lobe weight and pyramidal area.(1 point)
b) Calculate Pearson correlation coefficient. (1 point)

c) Calculate and write the equation of regression line of parietal lobe weight on pyramidal area. (2
points)
d) Give interpretation for the coefficient of determination (R 2 ) (1 point)
e) Predict parietal lobe weight for pyramidal area 8. (1 point)

Answer 1

Solution :

a)

b)

c)

d)

coefficient of determination r^2 = r * r = 0.9646 * 0.9646

coefficient of determination r^2 = 0.930

93.0% is explained and 7% is unexplained

e)

y = 2.877 + 15.467 * x

when x = 8

y = 2.877 + 15.467 * 8

yhat = 126.613