The quadratic regression equation that fits these data is y = 2.13x² + 0.13x + 6.39 option (D) is correct.
What is the line of best fit?
A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have data shown in the table:
X Values: -4, -3, -2, -1, 0, 1, 2, 3, 4
Y Values: 40, 28, 10, 8, 7, 10, 16, 26, 40
As we know, any equation of the form [tex]\rm cx^2+bx+a=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
The quadratic regression equation can be found as:
y = cx² +bx + a
For the value of a, b, and c:
From the table
a = 6.39
b = 0.13
c = 2.13
The quadratic regression is:
y = 2.13x² + 0.13x + 6.39
Thus, the quadratic regression equation that fits these data is y = 2.13x² + 0.13x + 6.39 option (D) is correct.
Learn more about the line of best fit here:
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