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Follow the below steps to use this calculator:

- Enter the data set
**X** - Enter the data set
**Y** - Hit the
**“Calculate”**button to get the answer - You can erase all the data by clicking on the
**“Reset”**button - No. of observations both in X and Y should be equal

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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. This quadratic equation models the relationship between two variables in the form of a parabola which is U shaped curve. This equation is used to make predictions or analyze trends.

Quadratic regression is a statistical method used to model the relationship between a dependent variable **(y) **and an independent variable **(x) **by fitting a quadratic ** (parabolic)** equation. This technique is useful when the data follows a curved rather than a straight line.

A quadratic equation is a mathematical expression that describes a parabolic relationship between two variables. The quadratic equation takes the form:

**Y = a + b(x) + c(x ^{2}) **

Where:

**Y**is the dependent variable.**X**is the independent variable.**a**,**b**, and**c**are the coefficients determined by the regression analysis.

The coefficients a, b, and $c$ can be calculated using the following formulas:

**b** = (S_{xy }S_{x}^{2}_{x}^{2 }– S_{x}^{2}_{y }S_{xx}^{2} ) / S_{xy }S_{x}^{2}_{x}^{2 }– (S_{xx}^{2})^{2}

**c** = (S_{x}^{2}_{y }S_{xx}^{ }– S_{xy }S_{xx}^{2} ) / S_{xy }S_{x}^{2}_{x}^{2 }– (S_{xx}^{2})^{2}

**a** = y - bx - cx^{2}

**$S$**is the sum of the product of x and y values.**S**is the sum of the squared $x$ values._{x}^{2}**S**is the sum of the fourth power of x values._{x}^{2}_{x}^{2}**S**_{x}^{2}_{y}_{}_{ }is the sum of the product of squared x and y values.**S**is the sum of the product of $x$ and squared x values._{xx}^{2}**x̄**is the mean of the x values.**ȳ**is the mean of the y values.**x̄**is the mean of the squared x values.^{2}

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.

S | S | S | S | S |

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 |

∑S | ∑S | ∑S | ∑S | ∑S |

**Step 4: **Calculate a, b, and c.

**For “b”:**

b = (S_{xy }S_{x}^{2}_{x}^{2 }– S_{x}^{2}_{y }S_{xx}^{2} ) / S_{xy }S_{x}^{2}_{x}^{2 }– (S_{xx}^{2})^{2}

b = {(-3.5) (129) – (-14.5) (25)} / {(5) (129) – (25)^{2}}

**b= -4.45**

**For “c”:**

c = (S_{x}^{2}_{y }S_{xx}^{ }– S_{xy }S_{xx}^{2} ) / S_{xy }S_{x}^{2}_{x}^{2 }– (S_{xx}^{2})^{2}

c = {(-14.5) (5) – (-3.5) (25)} / {(5) (129) – (25)^{2}}

**c = 0.75**

**For “a”:**

a = y - bx - cx^{2}

a = 5.75 – (-4) (2.5) – (0.75) (7.5)

**a = 11.25**

**Step 5: **Put the values in the formula.

y = ax^{2} + b(x) + c, where a ≠ 0

y = (11.25) x^{2} + (-4.45) x + (0.75)

*Quadratic regression* | Voxco

*A brief introduction to Quadratic regression *| Varsitytutors