Linear & Quadratic Regression

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the graph changes direction. It is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

What is the equation of a line of best fit?

Back

The equation of a line of best fit is a linear equation that best represents the data points in a scatter plot. It is often expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you calculate the linear regression equation from data?

Back

To calculate the linear regression equation, use the least squares method to minimize the sum of the squares of the vertical distances of the points from the line.

Front

What does a quadratic function model in real-life scenarios?

Back

A quadratic function can model various real-life scenarios, such as the trajectory of a projectile, the area of a square as a function of its side length, or profit maximization in business.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the significance of the coefficient 'a' in a quadratic function?

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 formula to find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) of a quadratic function in standard form f(x) = ax^2 + bx + c can be found using h = -b/(2a) and k = f(h).

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 more complex relationships between variables.

Front

What is the purpose of finding the line of best fit?

Back

The purpose of finding the line of best fit is to summarize the relationship between two variables and make predictions based on that relationship.

Front

How do you interpret the slope of a linear regression line?

Back

The slope of a linear regression line indicates the change in the dependent variable for each one-unit change in the independent variable.