Question

Use cubic regression to find a function that fits the following points. (-3, -28) (0, -4) (4, 168) (-5, -174) [ ? ]x3 + [ ]x2 + x + []

Answer 1

In blank spaces assume a,b,c,d

And equate this equation to y for solving the cubic regression

let -3,-28); (0,- 4); (4,168); (-5,2174) lan +6x² + (x + d = y – – – – from (0-4) não & y=-4 a.03 tb. 3 tcot d = - 4 -(from 1] Now Now E €3,-28) : x=-3, y=-28 a (-3)3 + b(-3)² + c(-3) + (-4) = -28 - [as d = -4] -27 a tab-3c - 4 =-28 - 27 a ta5-3c --24 = -9 a +3 bac=-8 (by dividing by 3) 99-35+= 820 When (4,168 ): x= 4, y = 168 = a (4)3 + b(4)2 + C(4) +(-4) = 168 = 64 a +16b + 4c - 4 =168 (de - 16a + 4b + a1 = 42 (dividing by 4) 16a +4b+c = 43) When 1-5, +174) - A(-s)² + 6(-5)² + ((-5) - 4 - - 174 -125a +255 -5C = -170 - 25a + 55-C = - 3.4 125a -sbtc - 34 - dividing by -sl

& solve equation a, qa-3b + c = 8 16a + 45+C = 43 259-5b+c= 34 ☺ - m m qa-3b + c =81 169 - 45 t C - 43 - + - - - 79 tb = - 35 Ta-b=357 Iba tabte = 43 2sa-sbtc - 34 -qa +95 = 9 I put a=6&b=7 in ) -ath = a-52-1] solve o b =at put b=atl es 7a-(a+1)=35 6a - 1 - 35 60 = 36 a=6 9(6)-3(7) +C = 8 54-21+c=8 c=8-33 (c =- 25 and a = - 4 is the beginny put a=6 en [h=1] in equation is 6x² + x2 + (x + (-4) = 6x² + 70² - 250 - 4
the equation of the function is:

6.r+ 7.– 25.0 – 4

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Answer 2

Use Cubic Regression to find a function that fits the following points