Question

2.1

#110. a) Use the regression procedures of Section R.6 to fit a cubic function y = f(x) to the data in the table, where x is daily caloric intake and y is life expectancy. Then fit a quartic function and decide which fits best.

b) What is the domain of the function?

c) Does the function have any relative extrema?

caloric intake and life expectancy

Country	daily caloric intake	life expectancy at birth (in years)	under-five mortality (number of deaths before age 5 per 1000 births)
Argentina	3030	76	14
Australia	3220	82	5
Bolivia	2100	66	51
Canada	3530	81	6
Dominican Republic	2270	73	25
Germany	3540	80	4
Haiti	1850	62	70
Mexico	3260	77	17
United States	3750	78	8
Venezuela	2650	74	16

Answer 1

(a) Cubic function: y = 0x^3 - 0.00001x^2 + 0.0586x - 10.69

(b) Quartic function: y = 0x^4 + 0.0000001x^3 - 0.0005x^2 + 0.8656x - 539.93

R^2 value is higher for the quartic function, so that is a better model

(b) Domains of both functions are [0, ∞)

(c) The cubic function has a local maximum at x = 2930, y = 75.16. The quartic function has no extrema.