Linear, Quadratic, & Exponential Regression

Front

What is a linear regression model?

Back

A linear regression model is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

Front

What is the general form of a quadratic equation?

Back

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

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = ab^x, where a is a constant, b is the base of the exponential, and x is the exponent.

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form y = ax² + bx + c can be found using the formula x = -b/(2a).

Front

What does the coefficient of x² represent in a quadratic equation?

Back

The coefficient of x² (a) determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the purpose of regression analysis?

Back

Regression analysis is used to determine the strength and character of the relationship between variables, allowing predictions based on data.

Front

What is the difference between linear and quadratic regression?

Back

Linear regression fits a straight line to data, while quadratic regression fits a parabolic curve, allowing for modeling of data with a U-shape.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x = 0, representing the starting point of the linear relationship on a graph.

Front

How can you determine if a relationship is exponential?

Back

A relationship is exponential if the ratio of the change in y to the change in x is constant, indicating a multiplicative growth pattern.

Front

What is the formula for the slope of a linear regression line?

Back

The slope (m) of a linear regression line is calculated as m = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²), where n is the number of data points.