# Describe relationship between variables

### The relationship between variables - Draw the correct conclusions

Statistical relationships between variables rely on notions of correlation and regression. These two concepts aim to describe the ways in which variables relate. Correlation is a statistical technique that is used to measure and describe a relationship between two variables. Usually the two variables are simply observed. As we have seen throughout this book, most interesting research questions in psychology are about statistical relationships between variables. Recall that there.

Correlation Correlation tests are used to determine how strongly the scores of two variables are associated or correlated with each other. A researcher might want to know, for instance, whether a correlation exists between students' writing placement examination scores and their scores on a standardized test such as the ACT or SAT. Correlation denotes positive or negative association between variables in a study.

Two variables are positively associated when larger values of one tend to be accompanied by larger values of the other.

The variables are negatively associated when larger values of one tend to be accompanied by smaller values of the other Moore An example of a strong positive correlation would be the correlation between age and job experience.

Typically, the longer people are alive, the more job experience they might have. An example of a strong negative relationship might occur between the strength of people's party affiliations and their willingness to vote for a candidate from different parties. In many elections, Democrats are unlikely to vote for Republicans, and vice versa. Regression Regression analysis attempts to determine the best "fit" between two or more variables. The independent variable in a regression analysis is a continuous variable, and thus allows you to determine how one or more independent variables predict the values of a dependent variable.

## Relationships Between Two Variables

Simple Linear Regression is the simplest form of regression. Like a correlation, it determines the extent to which one independent variables predicts a dependent variable. You can think of a simple linear regression as a correlation line.

The form or shape of a relationship refers to whether the relationship is straight or curved. A straight relationship is called linear, because it approximates a straight line. A curved relationship is called curvilinear, because it approximates a curved line.

### Psychological Statistics

An example of the relationship between the Miles-per-gallon and engine displacement of various automobiles sold in the USA in is shown below. This is curvilinear and negative. In this course we only deal with correlation coefficients that measure linear relationship.

There are other correlation coefficients that measure curvilinear relationship, but they are beyond the introductory level. The Degree Strength of a Relationship Finally, a correlation coefficient measures the degree strength of the relationship between two variables. The mesures we discuss only measure the strength of the linear relationship between two variables. Two specific strengths are: They are said to be perfectly linearly related, either positively or negatively.

### Relationships Between Two Variables | STAT

When two variables have no relationship at all, their correlation is 0. There are strengths in between Here are three examples: Weight and Horsepower The relationship between Weight and Horsepower is strong, linear, and positive, though not perfect.

Drive Ratio and Horsepower The relationship between drive ratio and Horsepower is weekly negative, though not zero.

The Pearson correlation coefficient is. The Pearson correlation coefficient is. Correlations can be used to help make predictions. If two variables have been known in the past to correlate, then we can assume they will continue to correlate in the future. We can use the value of one variable that is known now to predict the value that the other variable will take on in the future.

For example, we require high school students to take the SAT exam because we know that in the past SAT scores correlated well with the GPA scores that the students get when they are in college.

**How to Find the Relationship Between Two Variables, x and y.**

Suppose we have developed a new test of intelligence. We can determine if it is really measuring intelligence by correlating the new test's scores with, for example, the scores that the same people get on standardized IQ tests, or their scores on problem solving ability tests, or their performance on learning tasks, etc.

This is a process for validating the new test of intelligence. The process is based on correlation.