---from the CBS TV show, Numb3rs
Math is a priority goal for the school district. As a community service effort, then, we offer a very simple lesson in statistics, specifically linear regression and correlation. It all starts with a hypothesis, or theory. Our theory for today is that SPASD teachers salaries are so well correlated to years of experience, that we can generate a valid mathematical formula to calculate future salary!
First we plot the data: salary ($/hr) on the "y" or vertical axis, and years of experience on the "x" or horizontal axis. Then we perform a linear regression analysis on the data. We will "regress" the dependent variable, salary, against the independent variable, years of experience. The result of a linear regression is the equation of a line, in the form Y= mX+b (remember that?).
For SPEA, "Y" = salary ($/hr) and "X" = years of experience. Our data yields the regression equation, Salary = 0.8752 × years + 20.311. Recall from your math days that the "b" term is the 'y'-intercept. The "y' intercept represents the value on the "y" [salary] axis where X [years] equals zero. Here our "y" intercept is $20.311 per hour. Converting that to annual salary (multiply by 1520 hrs/yr), we get a salary of $30,873. Fancy that! That's just about precisely the base salary on the SPEA grid for 2009-10: $30,800. This is the bottom run of our SPEA salary grid. So far our regression equation is looking pretty accurate.
Another way we can evaluate the accuracy of a regression equation is to review the "correlation coefficient" for the data. The correlation coefficient is a mathematical equation that represents how well two variables [e.g. salary vs. yes of experience] correlate to one another. The value of the correlation coefficient is limited to values between −1.00 and +1.00. A perfect, positive correlation, where both variables rise at the same rate, is represented by a correlation of +1.00. Our correlation coefficient, denoted by the mathematical symbol "r", is 0.943. For a dataset of 540 points, a correlation coefficient of 0.943 is like having a credit score of 825. Money in the bank.
So, folks...wanna calculate your future earnings? Since contracts have been like clockwork, just multiply the number of years of service for that date in the future by 0.8752 and add 20.311. That represents your projected salary ($/hr) at that point in time.
Why should you care? Because here is the proof that it's not just a few lucky souls that earn a salary of over $70,000 at retirement. Just follow the arrow up from where it begins at the 30 years experience mark until it hits the (red) regression line. Then follow an arrow straight across to find a salary of about $46.50/hr, or $70,680 per year. So...you come out of school at age 24, work 30 years, and you're not even 55 and earning a salary over $70,000. And those are TODAY'S dollars.
As we continue the status quo, actual salaries are certain to continue to rise.
And that's why this should be more aptly termed, linear DEpression.
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