simple linear regression equation statistics

is included in the data set even though it is not technically a state.) ( skincancer.txt) (The data were compiled in the 1950s, so Alaska and Hawaii were not yet states, and Washington, D.C. The response variable y is the mortality due to skin cancer (number of deaths per 10 million people) and the predictor variable x is the latitude (degrees North) at the center of each of 49 states in the U.S. Here is an example of a statistical relationship. Instead, we are interested in statistical relationships, in which the relationship between the variables is not perfect. This course does not examine deterministic relationships. Boyle's Law: For a constant temperature, P = α/ V, where P = pressure, α = constant for each gas, and V = volume of gas.įor each of these deterministic relationships, the equation exactly describes the relationship between the two variables.

Ohm's Law: I = V/ r, where V = voltage applied, r = resistance, and I = current.

Hooke's Law: Y = α + β X, where Y = amount of stretch in a spring, and X = applied weight.

Here are some examples of other deterministic relationships that students from previous semesters have shared: That is, if you know the temperature in degrees Celsius, you can use this equation to determine the temperature in degrees Fahrenheit exactly. As you may remember, the relationship between degrees Fahrenheit and degrees Celsius is known to be:

Note that the observed ( x, y) data points fall directly on a line. Here is an example of a deterministic relationship. Types of relationshipsīefore proceeding, we must clarify what types of relationships we won't study in this course, namely, deterministic (or functional) relationships. In contrast, multiple linear regression, which we study later in this course, gets its adjective 'multiple,' because it concerns the study of two or more predictor variables. Simple linear regression gets its adjective 'simple,' because it concerns the study of only one predictor variable. The other terms are mentioned only to make you aware of them should you encounter them. The other variable, denoted y, is regarded as the response, outcome, or dependent variable.īecause the other terms are used less frequently today, we'll use the ' predictor' and ' response' terms to refer to the variables encountered in this course.One variable, denoted x, is regarded as the predictor, explanatory, or independent variable.Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables:

Simple linear regression equation statistics