SAT and Teacher Salaries

Solutions and Discussions


The primary goal was to analyze the relationship between teacher salaries and students' SAT performance with the intent of judging the validity of the "theory" mentioned in the problem, namely that states with well-paid teachers should have high performing students.

The data, however, suggest otherwise.   A scatterplot (shown below with the regression line superimposed) shows a roughly linear trend between average total SAT scores and average teacher salaries.  The trend, though not terribly strong, is decisively negative, which suggests that the states with higher paid teachers tended to have, on average, lower average SAT scores.

To quantify:  the correlation between SAT and salary is -0.44.  The regression equation is
(estimated SAT) = 1159 - 5.5*(average teacher salary)

Note that salaries are reported in thousands of dollars.  Hence this slope tells us that states with average teacher salaries 1000 dollars higher hadaverage SAT scores that were an average of 5.5 points lower than the states with lower-paid teachers.

Your report should show a scatterplot of total sat vs. salary.  (Use twoway (scatter total salary) (lfit total salary)  for example.)  This will show that California is somewhat in the middle of the pack, both in terms of salary and SAT performance.

For future reference, note that the trend might not be linear.  It seems that for states with lower salaries the SAT scores are mostly above the regression line; for states with middle-range salaries the SAT scores are mostly below the line; states with high salaries are mostly above the line.  This suggests that there might be a quadratic effect.  One way to examine this is to plot the residuals against the salary, but this was not required for this lab.

A similar pattern holds for Math and Verbal scores.

For Full Credit:

• You need to tell us what variables you examined (you might have also chosen math or verbal instead of total).  
•You should provide a scatter plot and a regression equation.
•  You should interpret the regression equation.
 Do NOT make the mistake of saying that as salary increases, SAT performance goes down.  The data do not tell us what happens when we increase salary.  Instead, they merely compare different states with different salaries.  When you compare States that differ in their average salary by $1000, you are not comparing teachers who saw their salary go up up $1000 but instead are comparing different States that can by thousands of miles apart and differ in very many ways as well.
• You must also have a conclusion that includes an explanation.  

 Here, it's clear that the theory is not true:  high paid teachers do not lead, necessarily, to high SAT scores.  But for full credit you must also give a plausible explanation of what might be going on.  And there are several approaches to this.  But first, its worth making some notes:

1)Remember that each data point consists of an average of very many schools from within a State. Thus, if we were to make a scatterplot of average teacher salary per school and average SAT score per school, the picture might be very different (and certainly there would be much less of an apparent trend.)
2) Remember that the data consist of a "snapshot" in time.  The theory mentioned in the problem statement -- high pay leads to high performance -- is NOT tested by these data.  To test that theory, you would have to examine how changing salary results in a change in performance.  States differ in many ways and the apparent relationship shown on this scatterplot could be caused by confounding factors.

With that in mind, there are several different explanations of what these data tell us.  One possibility is that States with difficult to teach schools must pay teachers more to get them to teach in those schools, and one might find that those schools have lower SAT scores.  If a state has many of these schools, then this would affect the average salary and SAT of the entire state.

There might be other reasons as well.  You are better economists than I, and so you might consider which market forces drive teacher salary (cost of living, location of school, etc) and see if you can think of a confounder that would explain why States with high average salaries tend to have lower SAT scores.
    Please make sure that your confounding variable makes logical sense.  Several students noted that high school students might have high SAT scores because of their enrollment in SAT coaching classes or other reasons that have nothing to do with the teachers.  Fine and good, but what does that have to do with this situation?  Just because lots of kids enroll in SAT coaching classes (and do you mean more kids in the entire State?  Or compared to other kids within the State?) doesn't explain why their teacher's make less money.  So you need an explanation that accounts for the relationship between the variables, not for any one variable alone.