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NORTH STAR METRIC Exclusive Step by Step guide to Descriptive Research Get ready to uncover the how, when, what, and where questions in a research
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Find the best survey software for you!
(Along with a checklist to compare platforms)
Take a peek at our powerful survey features to design surveys that scale discoveries.
Explore Voxco
Need to map Voxco’s features & offerings? We can help!
We’ve been avid users of the Voxco platform now for over 20 years. It gives us the flexibility to routinely enhance our survey toolkit and provides our clients with a more robust dataset and story to tell their clients.
Steve Male
VP Innovation & Strategic Partnerships, The Logit Group
Explore Regional Offices
Quadratic regression is a statistical technique used to find the equation of the parabola that best fits a set of data. This type of regression is an extension of simple linear regression that is used to find the equation of the straight line that best fits a set of data.
When illustrated on a scatter plot, a quadratic equation will form a “U” shape that is either concave down or concave up. Linear regression can be performed even with just two points, while quadratic regression requires many more data points. This is due to the fact that quadratic regression requires more data points to ensure that the data falls into the “U” shape.
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In quadratic regression, R-squared is the coefficient of the determination and it illustrates the degree to which the variation in y can be explained by x-variables. The r-squared value, therefore, allows us to evaluate how the differences in one variable can be explained by a difference in the second variable. R-squared can take values between 0 to 1, where 0 reflects 0% variation and 1 reflects a 100% variation.
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The equation used in quadratic regression is as follows:
y = ax2 + bx + c
The following formulas can be used to calculate the values of a, b, and c:
a = { [ Σ x2 y * Σ xx ] – [Σ xy * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] – [Σ xx2 ]2 }
b = { [ Σ xy * Σ x2x2 ] – [Σ x2y * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] – [Σ xx2 ]2 }
c = [ Σ y / n ] – { b * [ Σ x / n ] } – { a * [ Σ x 2 / n ] }
Where,
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Quadratic regression is a kind of statistical technique used to find the equation of the parabola that best fits a set of data.
Simple linear regression is used to find the equation of the straight line that best fits a set of data while quadratic regression is used to find the equation of the parabola that best fits a set of data.
The quadratic regression equation is;
y = ax2 + bx + c
Where,
a ≠ 0
Quadratic regression is used to model the relationship between two sets of variables so that the model can be used to explain or predict certain outcomes.
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