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Sagot :
The quadratic regression equation for this data set is [tex]\rm y=-0.143x^2+0.59x+2.82\\[/tex].
What is the general form of a quadratic equation?
The general form of the quadratic equation is given by;
[tex]\rm ax^2+bx+c=0[/tex]
Where; a, b, and c are the constants.
x; 0 1 2 3 4 5
y; 2.82 3. 29 3. 46 3. 33 2. 88 2. 24
From the table when the value of x = 0 the value of y is 2.82.
Then,
[tex]\rm y=ax^2+bx+c\\\\x=0\\\\2.82=a0^2+b(0)+c\\\\c=2.82[/tex]
From the table when the value of x = 3 the value of y is 3.33.
[tex]\rm y=ax^2+bx+c\\\\x=3\\\\2.82=a(3)^2+b(3)+c\\\\9a+3b+2.82=2.82\\\\9a=-3b\\\\b=-3a\\\\[/tex]
From the table when the value of x = 5 the value of y is 2.24.
[tex]\rm y=ax^2+bx+c\\\\x=3\\\\2.24=a(5)^2+(-3a)(5)+c\\\\25a-15a+2.82=2.24\\\\40a=2.24-2.82\\\\10a=-0.68\\\\a= \dfrac{-0.68}{10}\\\\a=-0.143[/tex]
And the value of b is;
[tex]\rm b=3a\\\\b=3(-0.14)\\\\b=0.59[/tex]
Therefore,
The quadratic regression equation for this data set is;
[tex]\rm y=ax^2+bx+c\\\\y=-0.143x^2+0.59x+2.82\\\\[/tex]
Hence, the quadratic regression equation for this data set is [tex]\rm y=-0.143x^2+0.59x+2.82\\[/tex].
To know more about the Quadratic equation click the link given below.
https://brainly.com/question/14935613
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