What is the quadratic regression equation for the data set?

(50, 10)

(30, 11)

(11, 5)

(35, 9)

(50, 12)

(20, 3)

(90, 7)

y = -0.546x² + 0.415x - 0.00367

Step-by-step explanation:

Quadratic Regression is a mathematical process to find a parabola that best fit a set of data. It has the form: y = ax² + bx + c

To find the equation, you have to solve the following system of equations:

a∑x⁴ + b∑x³ + c∑x² = ∑x²y

a∑x³ + b∑x² + c∑x = ∑xy

a∑x² + b∑x + cn = ∑y

To solve the system you have:

1) Make a table with 7 columns: for x-value, for y-values, for x² values, for x³ values, for x⁴ values, for x*y values and for x²y values.

2) Calculate each and in the last row, add all the values you found for each column. For example:

x                   y            x²            

50               10       2500

30               11         900

11                 5          121

35               9          1225

50               12        2500

20               3          400

90               7          8100

286            47         13246

3) Substitute the summations into the system of equations, knowing that 'n' is the number of items in the set

4) Solve it and determine the coefficients.

For this set of data, the coefficients are:

a = - 0.5458333

b = 0.41482696

c = - 0.003672

and the Quadratic Regresion Equation is:

- 0.546x² + 0.415x - 0.003672

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

answer: the correct answer is -32

step-by-step explanation: