Following is an example of output that might help a business be more productive.
Suppose a company develops a measure that combines experience and education into a single index. A decision is made to examine the degree to which this index relates to worker productivity. If the relationship is strong, the index can help the company form a decision rule for hiring potential employees.
First, the company might obtain a score for each current employee on a measure of worker productivity and the index of education/experience. These score can be plotted, summarized with a statistic, and be used to develop an equation for predicting one variable from the other.
Note that the relationship between the index of education/experience and worker productivity is positive. A positive relationship means that as one variable increases, the other variable increases. As one variable decreases, the other variable decreases. See the graph below.
Figure 1
The following table shows the ordinary Pearson "r" between the index of education and experience and worker productivity. Recall that the Pearson r is a descriptive statistic that measures the degree to which two variables follow a straight line. This statistic ranges from -1 to 1. Values close to -1 imply a strong negative linear relationship, values close to 1 imply a strong positive linear relationship, while values close to 0 suggest no linear relationship. This Pearson correlation is positive, which is consistent with the figure above, and fairly strong.
When squared, the Pearson correlation tells how how accurately the index of education/experience predicts worker productivity. When squared, the Pearson r tells the proportion of variance in one variable that is predictable from the other. In the context of this example, (.793)2 = .63 after rounding. This means that about .63 * 100 = 63% of the variance in worker productivity is accounted for by the index of education and experience. About 37% of the variance is not accounted for. Given that there is only a single predictor of worker productivity, this is a fairly accurate index.
Based on this information, a regression equation could be developed to predict worker productivity for future employees. This gives a predicted level of productivity given an individuals score on the index of education and experience. The regression equation for predicting worker productivity is
productivity = 3.496 (score on the index of education and experience) + 1.516
Suppose two individuals apply for a job. Applicant A scores an 8 on the index of education and experience while applicant B scores 6. We can derive employee predicted productivity scores using the equation above like this
Applicant A
= 3.496 (8) + 1.516
29.4 = predicted productivity score
Applicant B
= 3.496 (6) + 1.516
22.4 = predicted productivity score
On the surface, these predicted scores may not seem that different. To help interpret these scores, refer back to figure 1. Note that the predicted score for applicant A is associated with the most productive workers in the organization. The predicted score for applicant B is not bad, but it is only slightly above average.
Analyses such as these can be used to make better decisions. This process can be used in a wide variety of situations including:
- a measure of dexterity to predict assembly line output
- the use of demographic information to predict sales performance by region
- any number of quality control decisions
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