20 California Schools

Step 1: What Do We Want To Do?  

We want to answer the question: How does poverty relate to student performance in elementary schools?

Step 2: Formulate our Research Design and Specify the Econometric Model

20 CA Schools

The California state government assesses school performance using test scores as part of its accountability and continuous improvement system. Until 2013, the state computed an academic performance index (API) score for each school in the state. The API has been superceded by CALPADS in recent years.  We will use API data from elementary schools in 2013 to measure school performance. The API ranges from a low of 200 to a high of 1000.

The US National School Lunch Program provides free or reduced-price lunch to schoolchildren from low-income households. We observe the percent of students in each school who are eligible for free or reduced-price lunch (FLE). We will use this variable to approximate the degree of poverty in each school. 

We randomly selected 20 elementary schools in the state and recorded their API and FLE values. Data source.

The regression equation is \(API_i=b_0+b_1 FLE_i+e_i\)

Step 3: Apply Statistical Theory

Beginning in Chapter 4, we will learn how to use our results to make predictions about the other 5,745 CA elementary schools.


Using ordinary least squares, we obtain \(b_0=951.87\) and \(b_1=-2.11\).

Thus, if School A has a one unit higher FLE value than School B, then we predict that School A would have an API 2.11 points lower than School B.

The R-squared is 0.65. This model accounts for 65% of the variability in API scores across the 20 schools.

Data and Code

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