# Simple linear regression

Postassessment Statistical Sampling and Regression: Simple Linear Regression When you think of regressionthink prediction. Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous quantitative variables: One variable, denoted x, is regarded as the predictor, explanatory, or independent variable. The other variable, denoted y, is regarded as the response, outcome, or dependent variable. Because 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. The other terms are mentioned only to make you aware of them should you encounter them in other arenas. Simple linear regression gets its adjective "simple," because it concerns the study of only one predictor variable.

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.

Types of relationships Before proceeding, we must clarify what types of relationships we won't study in this course, namely, deterministic or functional relationships.

Here is an example of a deterministic relationship. Note that the observed x, y data points fall directly on a line. As you may remember, the relationship between degrees Fahrenheit and degrees Celsius is known to be: Here are some examples of other deterministic relationships that students from previous semesters have shared: For each of these deterministic relationships, the equation exactly describes the relationship between the two variables. This course does not examine deterministic relationships. Instead, we are interested in statistical relationships, in which the relationship between the variables is not perfect.

Here is an example of a statistical relationship. 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.

You might anticipate that if you lived in the higher latitudes of the northern U.

## Simple / Linear Regression Tutorial, Examples

The scatter plot supports such a hypothesis. There appears to be a negative linear relationship between latitude and mortality due to skin cancer, but the relationship is not perfect.

Indeed, the plot exhibits some "trend," but it also exhibits some "scatter. Some other examples of statistical relationships might include: Height and weight — as height increases, you'd expect weight to increase, but not perfectly.

## Related Calculators:

Alcohol consumed and blood alcohol content — as alcohol consumption increases, you'd expect one's blood alcohol content to increase, but not perfectly.

Vital lung capacity and pack-years of smoking — as amount of smoking increases as quantified by the number of pack-years of smokingyou'd expect lung function as quantified by vital lung capacity to decrease, but not perfectly.

Driving speed and gas mileage — as driving speed increases, you'd expect gas mileage to decrease, but not perfectly. Okay, so let's study statistical relationships between one response variable y and one predictor variable x!A simple linear regression uses only one independent variable, and it describes the relationship between the independent variable and dependent variable as a straight line.

This review will focus on the basic case of a simple linear regression. A regression line can show a positive linear relationship, a negative linear relationship, or no relationship.

Simple linear regression is the most commonly used technique for determining how one variable of interest (the response variable) is affected by changes in another variable (the explanatory variable). Linear regression consists of finding the best-fitting straight line through the points. The best-fitting line is called a regression line. The black diagonal line in Figure 2 is the regression line and consists of the predicted score on Y for each possible value of X. A simple linear regression is a method in statistics which is used to determine the relationship between two continuous variables. A simple linear regression fits a straight line through the set of n points.

If the graphed line in a simple linear regression is flat (not sloped), there is no relationship between the two variables. Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables: One variable, denoted x, is regarded as the predictor, explanatory, or independent variable.

Linear regression consists of finding the best-fitting straight line through the points. The best-fitting line is called a regression line. The black diagonal line in Figure 2 is the regression line and consists of the predicted score on Y for each possible value of X.

Linear regression is the technique for estimating how one variable of interest (the dependent variable) is affected by changes in another variable (the independent variable). If it is one independent variable, it is called as simple linear regression. In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables).The case of one explanatory variable is called simple linear pfmlures.com more than one explanatory variable, the process is called multiple linear regression.

Lesson 1: Simple Linear Regression | STAT