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The Quadratic regression calculator helps you evaluate the quadratic regression equation using data sets X and Y. It also shows a graph with a step-by-step solution.
The quadratic regression equation is
Y = a + b(x) + c(x2) where a
Here,
b = (Sxy Sx2x2 – Sx2y Sxx2 ) / Sxy Sx2x2 – (Sxx2)2
c = (Sx2y Sxx – Sxy Sxx2 ) / Sxy Sx2x2 – (Sxx2)2
a = y - bx - cx2
In the following example, the procedure to calculate the quadratic regression is explained briefly.
Example 1:
Determine a quadratic regression equation for the following data set of points.
(4,5),(3,6),(2,4),(1,8)
Solution:
Step 1: Separate the values
X= 4, 3, 2, 1
Y= 5, 6, 4, 8
Step 2: Calculate the mean of the datasets
Mean X = (4 + 3 + 2 + 1) / 4 = 5 / 2 = 2.5
Mean Y = (5 + 6 + 4 + 8) / 4 = 23 / 4 = 5.75
Step 3: Draw a table.
Sxx | Sxy | Sxx2 | Sx2x2 | Sx2y |
2.25 | -1.125 | 12.75 | 72.25 | -6.375 |
0.25 | 0.125 | 0.75 | 2.25 | 0.375 |
0.25 | 0.875 | 1.75 | 12.25 | 6.125 |
2.25 | -3.375 | 9.75 | 42.25 | -14.625 |
∑Sxx =5 | ∑Sxy = -3.5 | ∑Sxx2= 25 | ∑Sx2x2 = 129 | ∑Sx2y = - 14.5 |
Step 4: Calculate a, b, and c.
For “b”:
b = (Sxy Sx2x2 – Sx2y Sxx2 ) / Sxy Sx2x2 – (Sxx2)2
b = {(-3.5) (129) – (-14.5) (25)} / {(5) (129) – (25)2}
b= -4.45
For “c”:
c = (Sx2y Sxx – Sxy Sxx2 ) / Sxy Sx2x2 – (Sxx2)2
c = {(-14.5) (5) – (-3.5) (25)} / {(5) (129) – (25)2}
c = 0.75
For “a”:
a = y - bx - cx2
a = 5.75 – (-4) (2.5) – (0.75) (7.5)
a = 11.25
Step 5: Put the values in the formula.
y = ax2 + b(x) + c, where a ≠ 0
y = (11.25) x2 + (-4.45) x + (0.75)
Quadratic regression | Voxco
A brief introduction to Quadratic regression | Varsitytutors
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