Quadratic Regression

Front

What is a quadratic regression?

Back

A quadratic regression is a type of regression analysis used to model the relationship between a dependent variable and an independent variable by fitting a quadratic equation to the data.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the coefficient 'a' in a quadratic equation indicate?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is a curve of best fit?

Back

A curve of best fit is a smooth curve that best represents the data points in a scatter plot, often determined using regression analysis.

Front

How do you interpret the coefficients in a quadratic regression model?

Back

The coefficients represent the impact of the independent variable on the dependent variable: 'a' affects the curvature, 'b' affects the slope, and 'c' is the y-intercept.

Front

What is the purpose of using quadratic regression?

Back

Quadratic regression is used to model relationships where the effect of the independent variable on the dependent variable is not constant, allowing for acceleration or deceleration.