Consider the regression model fit to the nisin extraction data in Exercise 12-18. Use nisin extraction as the response.

(a) Test for significance of regression using α = 0.05. What is the P-value for this test?

(b) Construct a t-test on each regression coefficient. What conclusions can you draw about the variables in this model? Use α = 0.05.

(c) Comment on the effect of a small sample size to the tests in the previous parts.

Exercise 12-18

An article in Biotechnology Progress (2001, Vol. 17, pp. 366€“368) reported on an experiment to investigate and optimize nisin extraction in aqueous two-phase systems (ATPS). The nisin recovery was the dependent variable (y). The two regressor variables were concentration (%) of PEG 4000 (denoted as x₁ and concentration (%) of Na2SO4 (denoted as x₂). The data are in Table E12-10.

y X1 X2 62.8739 13 11 11 15 76.1328 13 13 87.4667 15 13 102.3236 76.1872 14 12 77.5287 14 12 14 12 76.7824 14 12 77.4381 12 14 78.7417