Answer: 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
