Question

Determine the quadratic regression for the data.

Answer 1

{ solution is attached below}

Answer 2

Answer:

$y = 0.27\cdot x^{2} - 2.44\cdot x + 7.49$

Step-by-step explanation: The quadratic regression is given by :

$y = a\cdot x^{2} +b\cdot x + c$

In order to get the quadratic regression equation we need to simplify :

$a\cdot \sum {x_i}^{4}+b\cdot \sum {x_i}^{3}+c\cdot \sum {x_i}^{2}=\sum {x_{i}}^{2}\cdot y_{i}\\a\cdot \sum {x_i}^{3}+b\cdot \sum {x_i}^{2}+c\cdot \sum {x_i}=\sum {x_{i}}\cdot y_{i}\\a\cdot \sum {x_i}^{2}+b\cdot \sum {x_i}+c\cdot {n_i}=\sum y_{i}$

⇒

$3364\cdot a+560\cdot b+100\cdot c=303\\560\cdot a +100\cdot b+20\cdot c=59\\100\cdot a +20\cdot b +5\cdot c=16$

On solving this system of equation, we get a = 0.27 , b = - 2.44 , c = 7.49

Hence, the required quadratic regression is $y = 0.27\cdot x^{2} - 2.44\cdot x + 7.49$