Correlations and Regression

This will be a brief tutorial, since there is very little that is required to calculate correlations and linear regressions. To calculate a simple correlation matrix, one must use [Statistics => Correlate => Bivariate...], and [Statistics => Regression => Linear] for the calculation of a linear regression.

For this section, the analyses presented in the computer section of the Correlation and Regression chapter will be replicated. To begin, enter the data as follows,

 IQ GPA 102 2.75 108 4.00 109 2.25 118 3.00 79 1.67 88 2.25 ... ... ... ... 85 2.50

Simple Correlation

• Click on [Statistics => Correlate => Bivariate...], then select and move "IQ" and "GPA" to the Variables: list. [Explore the options presented on this controlling dialog box.]

• Click on [OK] to generate the requested statistics.
The results from output window should look like the following,

As you can see, r=0.702, and p=.000. The results suggest that the correlation is significant.

Note: In the above example we only created a correlation matrix based on two variables. The process of generating a matrix based on more than two variables is not different. That is, if the dataset consisted of 10 variables, they could have all been placed in the Variables: list. The resulting matrix would include all the possible pairwise correlations.

Correlation and Regression

Linear regression....it is possible to output the regression coefficients necessary to predict one variable from the other - that minimize error. To do so, one must select the [Statistics => Regression => Linear...] option. Further, there is a need to know which variable will be used as the dependent variable and which will be used as the independent variable(s). In our current example, GPA will be the dependent variable, and IQ will act as the independent variable. Specifically,

• Initiate the procedure by clicking on [Statistics => Regression => Linear...]

• Select and move GPA into the Dependent: variable box

• Select andmove IQ into the Independent(s): variable box

• Click on the [OK] to generate the statistics.

Note: A variety of options can be accessed via the buttons on the bottom half of this controlling dialog box (e.g., Statistics, Plots,...). Many more statistics can be generated by explore the additional options via the Statistics button.

Some of the results of this analysis are presented below,

The correlation is still 0.702, and the p value is still 0.000. The additional statistics are "Constant", or a from the text, and "Slope", or B from the text. If you recall, the dependent variable is GPA, in this case. As such, one can predict GPA with the following,

GPA = -1.777 + 0.0448*IQ

The next section will discuss the calculation of the ANOVA.