Page 60 - Quality control of pharmaceuticals (07-PA 704)
P. 60
Determine the correlation coefficient, r
Find the regression equation.
The data are presented in a table as follows:
Xi Yi (Xi- ̅ ) ( − ̅ )2 (Yi- ̅ ) ( − ̅ )2 (Xi- ̅ ) (Yi- ̅ )
0 2.1 -6 36 -11.0 121.0 66.0
2 5.0 -4 14 -8.1 65.61 32.4
4 9.0
6 12.6
8 17.3
10 21.0
12 24.7
Sum: 42 91.7 0 0 112 418.28 216.2
The figures below the line at the foot of the column are in each case the sums of
the figures in the table.
r= ∑ {( − ̅ )( − ̅ )}
{[∑ ( − ̅ )2][∑ ( − ̅ )2]}12
r = 216.2 = 216.2 = 0.9989
√112 ×418.28 216.44
Slope of least squares line: b = ∑ {( − ̅ )( − ̅ )
∑ ( − ̅ )2
b = 216.2/112 = 1.93
Intercept of least squares line: a = ̅ − ̅
∴ = 13.1 − (1.93 × 6) = 13.1 − 11.58
