Part 2. MM4XL Tools > 2. Analytical Tools > CrossTab > 3. Technicalities > Testing variables for correlation (Pearson)
## CrossTab ### Testing variables for correlation (Pearson) Using both *R* and *R*^{2} coefficients, CrossTab can test the correlation between variables of each table it prints. The **Pearson Product Moment Correlation Coefficient,** *R*. *R* is an index ranging from -1.0 to 1.0 and reflects the extent of a linear relationship between two data sets. Panels A, B, and C in the picture below show the three different types of association between variables. In panel A, *R* = 1 represents perfect positive association between variables, which means Y increases in a perfectly predictable manner as X increases. Panel B, *R* = 0.8, shows a strong relationship as well, but of a negative nature so as X increases Y decreases. Finally, panel C, *R* = 0, show two unrelated variables. The Correlation Coefficient, however, does not tell us much about the strength of the relationship between variables, which can be measured with the **Coefficient of Determination, ***R*^{2}. *R*^{2}measures the proportion of variation explained by the independent variable. The proportion 1-*R*^{2}is the part of variation explained by factors other than what is accounted for by the two variables we use. Panel B, for instance, could refer to the part of variability explained by the model and referring to daily sales and number of clients served. *Note:* CrossTab prints the correlation and determination coefficients only when the input data is numerical. They are skipped when the data is in string (text) form. From the table above we see R = 0.094 and R squared = 0.009. This means it has not been found any association between the language clients speak and the class they belong to. So, unfortunately, we cannot use the variable Language to predict clients class membership. |