Question

Use cubic regression to find a

Answer 1

Answer:

$y = x^{3} -\frac{26}{5}x^{2}-7x+\frac{11}{5} =x^{3}-5.2x^{2}-7x+2.2$

Step-by-step explanation:

$y = ax^{3}+bx^{2}+cx+d\\(1, -9) => -9 = a + b + c + d \\(-1, 3)=> 3 = -a +b-c+d\\Add => 2b+2d = -6 => b+d=-3\\=> a+c = -6\\\\(2, -15) => -15 = 8a+4b+2c+d\\(3, -29) => -29 = 27a+9b+3c+d\\Subtract => 19a+5b+c = -14\\Substitute (c = -6 -a) => 18a+5b=-14\\b=\frac{-14-18a}{5}\\\\8a + 4b +2c + d = -15 => Substitute => 8a + 4( \frac{-14-18a}{5})+2(-6-a)+(-3-\frac{-14-18a}{5}) = 15 => Simplify => -\frac{24}{5}a-\frac{99}{5} = -15 => a = 1\\b=-\frac{26/5}\\c=-7\\d=\frac{11}{5}$