Find Good Schools Using Data - Part Two

24 September 2012

"You'll love this expensive neighborhood. It has great schools"  - Every Realtor, ever


This is the second blog post analyzing the quality of schools using data. In the last post we identified a key success metric and saw the quality of schools. Now we'll ask: Are good schools always in expensive neighborhoods?

WARNING: Correlation != causation. We'll see correlations between housing prices and school quality. This does not mean school quality changes because of the price of a house. Children don't become better students because their bedroom has fancier paint.


When parents buy a house, a 'good neighborhood'  means 'near good schools'. Parents will spend as much as they can afford to be near a good school. Let's see if it's a good idea to spend more; below is a graph of schools' High Achiever % compared with house prices.

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There is a rough trend where school quality increases as house prices increase. Let's see how much of a trend there is. A little linear math (least squares' regression) produces this equation.

High Achiever % = Median House Price * 0.0000002439 - 0.0274391
R^2 = 0.259, SSE = 0.818, MSE = 0.00223, p-value = < 0.0001

An R² value of 1 means two variables are perfectly correlated. An R² value of 0 means no correlation. Here there is a correlation of 0.259. The p-value is very small (less than 0.05), meaning that the linear regression is probably significant. So, we're not grasping at straws.

We're interested in schools with a high High Achiever % that is not due to house prices. This is also known as the residual

High Achiever % Not Due To House Prices = 
High Achiever %  - High Achiever % Due to House Prices (equation)
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This is the same data as above, except without the influence of house prices. Here we can see which schools are good deals; they have positive values.

For example, Mercer Island high school has a 16% High Achiever value, which is quite good. However, it is a very low score for the cost, because the median house costs over $1 million. Therefore its residual value is negative (it's not worth the price). In contrast, Friday Harbor high school has a 27% High Achiever value, with a median house price of around $360K. It's a far better deal.

Parents could use this data to make informed decisions about where to move. For example, we can see that houses over $400K don't provide much (if any) additional improvement in school quality.

Rent Prices

What if we want to rent, instead of buying? Let's look at school quality compared to rent price:

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There is a correlation between rental prices and school quality. More linear math, and we find:

High Achiever % = Average Rent * 0.0001197 - 0.0684526
R^2 = 0.247, SSE = 0.724, MSE = 0.00282, p-value = < 0.0001

There is still a correlation, but it's weaker compared to house prices (an R² value of .247 instead of .259). Still, we can use the linear equation to plot the residual, looking for good deals:

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The correlation (R²) between rent and school quality is weaker than between house prices and school quality. There are more potential deals when renting instead of buying.

The Takeaway: Don't assume schools are better because they're in a pricier neighborhood; that's not always true. And consider renting instead of buying.

What's Next

Sometimes we don't have to dig too deeply. This basic level of analysis is sufficient for parents on a budget.

However, there is a lot more insight in this data. In the next post we will look at which factors influence school quality. Stay tuned for more data!