Irfan Ahmed, PhD

Regression is a statistical tool that allows you to predict the value of one continuous variable from one or more other variables. When you perform a regression analysis, you create a regression equation that predicts the values of your DV using the values of your IVs. Each IV is associated with specific coefficients in the equation that summarizes the relationship between that IV and the DV. Once we estimate a set of coefficients in a regression equation, we can use hypothesis tests and confidence intervals to make inferences about the corresponding parameters in the population. You can also use the regression equation to predict the value of the DV given a specified set of values for your IVs. Simple Linear Regression Simple linear regression is used to predict the value of a single continuous DV (which we will call Y) from a single continuous IV (which we will call X). Regression assumes that the relationship between IV and the DV can be represented by the equation. Y i = β 0

Pearson correlation A Pearson correlation measures the strength of the linear relationship between two continuous variables. A linear relationship is one that can be captured by drawing a straight line on a scatterplot between the two variables of interest. The value of the correlation provides information both about the nature and the strength of the relationship. • Correlations range between -1.0 and 1.0. • The sign of the correlation describes the direction of the relationship. A positive sign indicates that as one variable gets larger the other also tends to get larger, while a negative sign indicates that as one variable gets larger the other tends to get smaller. • The magnitude of the correlation describes the strength of the relationship. The further that a correlation is from zero, the stronger the relationship is between the two variables. A zero correlation would indicate that the two variables aren’t related to each other at all. Correlations only measure the strength