Statistics: Simple Linear Regression

Try these parameter values:

Negative Functional Relationship

slope -0.5

intercept: 4

Positive Functional Relationship

slope: 0.5

intercept: 4

Statistics: Simple Linear Regression

Typically, a simple linear regression is performed when one wishes to determine the functional linear relationship between an independent variable and a dependent variable. This relationship is best expressed in an equation of the form:

An equation of this form is valuable because it can be used to predict the value of the dependent variable (Y), given a value of the independent variable (X). The slope (b) and the Y intercept (a) of this best fit line are calculated as follows:

Statistics: Simple Linear Regression

Adjust the slope and intercept of the best-fit line to the right:

Notice that the slope and Y-intercept are independent of each other.

Also note that the equation for the best-fit line indicates the functional relationship between the independent and dependent variables, and not how well the points fit to the regression line.