Interpreting percentage units regressions

Question

I am using a panel of 2249 schools with data from 2002-2008. Some of the schools are single sex schools whilst others are mixed sex.

Some background on my regression:

Consider the determinants of school performance (as measured by the percentage of pupils in the school who get 5 A*-C grades at GCSE: sch5ac). Start by using the following explanatory variables:

-stdschk2aps: a measure of the academic performance of pupils when they enter the school. The variable has been standardised to have mean zero and standard deviation one.

-schfsm: the percentage of pupils in the school who are eligible for free school meals; this can be thought of as a proxy for the proportion of pupils from low income families.

-schsen: the percentage of pupils in the school classified as having special educational needs (i.e. requiring additional support). Schools receive extra funding to help support these pupils.

I am asked to estimate the effect of each of these variables on the dependent variable (sch5ac) for the single sex schools, using the within estimator.

sch5ac=beta_0+beta_1*schsen+beta_2*schfsm+beta_3*stdschk2aps

I get the following coefficients:

beta_1= 0.215

beta_2= -0.357

beta_3= 6.935

Both schsen and schfsm are measured as a percentage, as is the dependent variable sch5ac. So would a 1% increase in schsen lead to a 0.215% increase in sch5ac?

Since stdschk2aps is not measured as a %, but the dependent variable sch5ac is, would a unit increase in stdschk2aps increase sch5ac by 6.935 percentage points?

Any help would be great, Thanks Kai

Answer 1

That is the correct interpretation of your results.

However, it may not be appropriate to use OLS regression when the dependent variable is a percentage, there may be ceiling and floor effect, ridiculous predictions (> 100 or < 0), and the assumptions are likely to be violated.

Beta regression is probably better suited to your problem.