Regression Review

A linear regression equation is a mathematical representation of the relationship between two variables, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

To predict values, substitute the independent variable (x) into the linear regression equation and solve for the dependent variable (y).

The slope represents the rate of change of the dependent variable (y) for each unit change in the independent variable (x).

The y-intercept is the value of y when x is 0, indicating where the line crosses the y-axis.

A correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables, ranging from -1 to 1.

A correlation coefficient of -0.75 indicates a strong negative correlation, meaning as one variable increases, the other variable tends to decrease.

Linear regression models a straight-line relationship, while exponential regression models a relationship where the rate of change increases or decreases exponentially.

An exponential regression model typically shows a curve that rises or falls sharply, indicating rapid growth or decay.

The general form of an exponential regression equation is Y = a(b^x), where a is a constant and b is the base of the exponential function.

Exponential growth refers to an increase that occurs at a rate proportional to the current value, leading to rapid increases over time.