Answer: the regression model for the given table is y = 22x^2 + 7x - 2.
Explanation:
We can use the method of least squares to find the regression model of the table. The regression model is of the form y = ax^2 + bx + c, where a, b, and c are constants to be determined.
First, we can find the values of the sums:
Σx = 10
Σy = 682
Σx^2 = 30
Σy^2 = 71684
Σxy = 1462
Next, we can use these values to find the values of a, b, and c:
a = [nΣxy - (Σx)(Σy)] / [nΣx^2 - (Σx)^2]
= [(5)(1462) - (10)(682)] / [(5)(30) - (10)^2]
= 22
b = [Σy - aΣx^2 - cΣx] / n
= [682 - (22)(30) - c(10)] / 5
= 7
c = [Σy - aΣx^2 - bΣx] / n
= [682 - (22)(30) - (7)(10)] / 5
= -2