# Relationship between test and regression

### Correlation and Regression

The tests are used to conduct hypothesis tests on the regression Failure to reject implies that no linear relationship exists between and. An example of a t test research question is “Is there a significant difference between the reading scores of boys and girls in sixth grade?” A sample answer might. Roughly speaking: the t-test (comparing two groups) is a special case of ANOVA (comparing several groups) which is a special case of multiple regression.

### Statistics review 7: Correlation and regression

While EPSY is not intended to be a statistics class, some familiarity with different statistical procedures is warranted. In order to calculate a t test, we need to know the mean, standard deviation, and number of subjects in each of the two groups. The 23 is the degrees of freedom for a t test. It is the number of subjects minus the number of groups always 2 groups with a t-test.

You may wish to review the instructor notes for t tests. The first number is the number of groups minus 1.

## ANOVA, Regression, and Chi-Square

The second number is the total number of subjects minus the number of groups. Because we had subject and 3 groups, it is ]. One for each of the two independent variables and one for the interaction of the two independent variables. Do Democrats, Republicans, and Independents differ on their opinion about a tax cut? Do males and females differ on their opinion about a tax cut? Is there an interaction between gender and political party affiliation regarding opinions about a tax cut?

A two-way ANOVA has three null hypotheses, three alternative hypotheses and three answers to the research question. The answers to the research questions are similar to the answer provided for the one-way ANOVA, only there are three of them.

Investigating Relationships Simple Correlation Sometimes we wish to know if there is a relationship between two variables. A simple correlation measures the relationship between two variables. The variables have equal status and are not considered independent variables or dependent variables. While other types of relationships with other types of variables exist, we will not cover them in this class.

### ANOVA, Regression, and Chi-Square | Educational Research Basics by Del Siegle

A canonical correlation measures the relationship between sets of multiple variables this is multivariate statistic and is beyond the scope of this discussion. Regression An extension of the simple correlation is regression. In regression, one or more variables predictors are used to predict an outcome criterion.

Data for several hundred students would be fed into a regression statistics program and the statistics program would determine how well the predictor variables high school GPA, SAT scores, and college major were related to the criterion variable college GPA. Not all of the variables entered may be significant predictors. R2 tells how much of the variation in the criterion e. The regression equation for such a study might look like the following: For example, someone with a high school GPA of 4.

For example, a medical researcher might want to use body weight independent variable to predict the most appropriate dose for a new drug dependent variable.

The purpose of running the regression is to find a formula that fits the relationship between the two variables. Then you can use that formula to predict values for the dependent variable when only the independent variable is known. A doctor could prescribe the proper dose based on a person's body weight. The regression line known as the least squares line is a plot of the expected value of the dependent variable for all values of the independent variable. Technically, it is the line that "minimizes the squared residuals".

The regression line is the one that best fits the data on a scatterplot. Using the regression equation, the dependent variable may be predicted from the independent variable.

## Correlation and Regression

The slope of the regression line b is defined as the rise divided by the run. The y intercept a is the point on the y axis where the regression line would intercept the y axis. The slope and y intercept are incorporated into the regression equation.