Linear, Quadratic, Exponential Regression

Front

What is correlation in statistics?

Back

Correlation measures the strength and direction of a linear relationship between two variables. It can be positive, negative, or no association.

Front

What does a linear regression equation represent?

Back

A linear regression equation represents the relationship between a dependent variable (y) and an independent variable (x) in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does an R-squared (R²) value of 1 indicate?

Back

An R-squared value of 1 indicates that the regression line perfectly fits the data points, meaning all points lie exactly on the line.

Front

What is the line of best fit?

Back

The line of best fit is a straight line that best represents the data on a scatter plot, minimizing the distance between the line and all data points.

Front

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

Back

The slope (m) of a linear regression line is calculated using the formula m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2), where n is the number of data points.

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 a U-shaped relationship.

Front

What is an exponential regression model?

Back

An exponential regression model describes data that grows or decays at a constant percentage rate, typically represented as y = ab^x, where a is a constant and b is the base of the exponential.

Front

What does it mean if a regression line has a negative slope?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases, showing an inverse relationship.

Front

What is the purpose of regression analysis?

Back

Regression analysis is used to understand the relationship between variables, make predictions, and identify trends in data.

Front

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

Back

The y-intercept (b) in a regression equation represents the value of the dependent variable when the independent variable is zero.