Linear Regression
The third volume in a series of Advanced Educational Statistics, Linear Regression maintains the no nonsense teaching methodology for learning educational statistics. A narrative, along with videos, output data sets and sample data sets are included. As with previous volumes in the series, the video presentations are the focal point and will be especially helpful for guiding the learner through the process of conducting statistical analyses using SPSS and interpreting SPSS output data.
Linear regression is a prediction model in which one variable is used to predict a second variable. If the variables are highly correlated, the linear model is strong. If the variables are poorly coordinated, the linear model is weak. Linear regression is used to create a line of best-fit. This line minimizes the distance between the linear model and each of the data points. To understand more about the power of this model, a brief review of linear functions may prove helpful. Linear functions are a special type of algebraic function. An algebraic function is a relationship having two distinct variables. One of the variables, the independent variable (x), creates the other variable, the dependent variable (y). To be a function, each x must map to only one y. Another way of saying this is that each x value can only go to one location at a time. The following video helps to explain the concept of a linear function.
The line of best-fit is the linear function which best fits a given set of data points. The best-fit line minimizes the distance of the linear regression model to each of the indicated points. To better understand this concept, please view the video below.
As with other methodologies of quantitative design, linear regression requires the construction of research questions. These research questions are founded upon correlational relationships though the linear regression model is being used for prediction. Consider the following video.
Linear regression requires that the two variables be reasonably correlated. The level of correlation is often driven by the problem. Do you remember the Pearson r? What about the Kendall Tau or the Spearman Rho? Correlation is important. Note that correlation is an assumption of linear regression. If the variables are not correlated, a linear regression model makes no sense. Now, let us examine the process for using SPSS to conduct simple linear regression in the video below.
The SPSS readout provides a lot of information. Some of that information is necessary to develop the linear regression model. Some of it is not. You must be able to select those items of value to your research. The video below examines the SPSS readout to develop the appropriate linear regression model. Linear regression is a powerful tool; however, remember that the model only works between the lower bound and the upper bound of the data set. Speculation beyond these values is meaningless.