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(-2,-16)(1,5)(3,59)(6,440)

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Answer:

The cubic regression that fits the points (x,y) =(-2,-16), (x,y) = (1,5), (x,y) = (3, 59) and (x,y) =(6,440) is y =2\cdot x^{3}+x+2.

Step-by-step explanation:

A cubic polynomial is a polynomial that has the following form:

y = a\cdot x^{3}+b\cdot x^{2}+c\cdot x + d (1)

Where:

x - Independent variable, dimensionless.

y - Dependent variable, dimensionless.

a, b, c, d - Coefficients, dimensionless.

We construct the following system of equations to determine the coefficients of the cubic regression:

(x,y) =(-2,-16)

-8\cdot a +4\cdot b -2\cdot c + d = -16 (1)

(x,y) = (1,5)

a+b+c+d= 5 (2)

(x,y) = (3, 59)

27\cdot a + 9\cdot b + 3\cdot c + d = 59 (3)

(x,y) =(6,440)

216\cdot a + 36\cdot b + 6\cdot c + d = 440 (4)

The solution of the system of linear equations is:

a = 2, b = 0, c = 1, d = 2

The cubic regression that fits the points (x,y) =(-2,-16), (x,y) = (1,5), (x,y) = (3, 59) and (x,y) =(6,440) is y =2\cdot x^{3}+x+2.

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answered 9 months ago