Question

Table on the right shows the per capita consumption of ice cream and eggs for selected years since 1980. Per Capita Consumption Complete parts (A) and (B). of Ice Cream and Eggs Ice Eggs Year cream (number) (pounds 1980 16.5 266 1985 17.8 251 1990 16.3 231 1995 15.1 229 200g 16.4 247 2005 13.6 | 252 2010 12. 8 242 (A) Let x represent the number of years since 1980 and find a cubic regression polynomial for the per capita consumption of ice cream The cubic regression is y=[x-x x-17 (Round to four decimal places as needed)

Answer 1

| у 16.5 17.8 | 10 | 16.3 | 15 | 15.1 x^2 | x^3 | x^4 | x^5 | x^6 | x*y | x^2 *y | x^3 *y. о о о о о о то 25 125 625 13125 15625 89 445 | 2225 100 1000 10000 1 100000 1000000 163 1630 16300 225 3375 50625 759375 111390625 226.5 3397.5 1 50962.5 400 8000 160000 | 3200000 | 64000000 328 6560 | 131200 625 15625 390625 | 9765625 | 244140625 | 340 8500 | 212500 900 27000 810000 24300000| 729000000 | 384 11520 345600 2275 155125 | 1421875 | 38128125 1049546875 1530.5 | 32052.5 | 758787.5 | 20 25 16.4 13.6 12.8 108.5 | Total | 105

Let required equation is Let y = a +bx+cx^2 + d x*3 normals equations are y=n*a+b+ 2(x) + *2x^2)+d* (x^3) E(x * y) = a* 3(x) + b* 3(x^2)+c* 3(x^3) + d * 3(x^4) 3(x^2 * y) = a * 3(x^2)+b* (x^3) +c* 3(x^4) + d * 3(x^5) 3(x^3 * y) = a * [(x^3) +b * (x^4) +c * 3(x^5) + d * 3(x^6) equations are 7 a +105 b + 2275 C +55125 d = 108.5 105 a + 2275 b +55125 C +1421875 d = 1530.5 2275 a +55125 b + 1421875 C +38128125 d = 32052.5 55125 a +1421875 b +38128125 C +1049546875 d = 758787.5

On solving a = 16.7976 b = 0.0773 C=-0.0097 d = 0.0001 Required curve is y = 16.7976 +0.0773 x -0.0097 x^2 +0.0001 x^3 y = 0.0001 x^3 -0.0097 x^2 +0.0773 x + 16.7976 answer