Get the Data
For historical home price data I went to the most widely recognized gauge of U.S. home prices, the S&P/Case-Shiller U.S. National Home Price Index, and found a data set for the monthly value of the index dating back to 1975. The St. Louis Fed publishes the raw Case-Shiller home price index data and makes it easy to download. For historical mortgage rate data, I found that Freddie Mac provides historic tables of monthly mortgage rates dating back to 1971, and their site links to the raw data in spreadsheets. I downloaded the history table for the 30 Year Fixed-Rate Mortgage and focused on 1975 to the present to line up the dates in the two data sets.
Formulate a Question
Before getting into the data, I asked a few basic questions: do rates affect home prices? If so, how? More specifically, are the two variables correlated in any way? What can we expect from home prices if rates go up?
Explore the Data
To get a better sense for the range of values in the data and where we are today, I looked for the mean, min, max, and current values as well as the years in which the top and bottom of the range of values in both variables occurred:
Interest Rates
From January 1975 to August 2016:
| Mean | 8.3 |
| Min | 3.3 (2012) |
| Max | 18.4 (1981) |
| Current | 3.4 |
| Standard Deviation | 3.2 |
Home Prices
From January 1975 to August 2016:
| Mean | 97.5 |
| Min | 25.2 (1975) |
| Max | 184.6 (2006) |
| Current | 184.4 |
| Standard Deviation | 48.3 |
The range of values in the data shows that the fixed-rate on a 30 year mortgage is almost as low today as it was at the very bottom of it’s recorded history in 2012. Also, the Case-Shiller Home Price Index is currently just .2 away from it’s highest point ever recorded since 1975, very close to the peak of the housing bubble in 2006. So we are near historical lows for rates and historical highs for prices. Or, as a statistician might put it: we are looking at the tail ends of the distribution.
Rates are currently one and a half standard deviations below the mean, while the Home Price Index is nearly two standard deviations above the mean.
Prepare the Data
I merged the two data sets into a single, 3-column table that has a row for every month of the year from January 1975 to August 2016:
| D | X | Y |
|---|---|---|
| 1/1/1975 | 9.43 | 25.25 |
| 2/1/1975 | 9.10 | 25.29 |
| 3/1/1975 | 8.89 | 25.36 |
| ... | ||
| 6/1/2016 | 3.57 | 182.19 |
| 7/1/2016 | 3.44 | 183.43 |
| 8/1/2016 | 3.44 | 184.42 |
Where D is a date, X is the rate, and Y is the housing index value.
Regression Analysis
To see if rates affect prices, we plot Y, the housing index value, as a dependent variable and X, the rate, as an independent variable. Since we think X has an impact on Y, we can use R to do a simple linear regression analysis on the data.
In the plot, a regression line, the best-fitting line that minimizes the sum of the squares of the vertical distances from each data point to the line, explains the relationship between the two variables. It slopes down. When y-axis values are high, x-axis values tend to be low; when y-axis values are very low, x-axis values are very high. Clearly, there is a strong negative correlation between the two variables and the data visualization makes this plain to see. A strong negative correlation only suggests that high values for X are associated with low values for Y. This is demonstrated by 41 years of data analyzed here. But a strong negative correlation does not imply that X causes Y. In other words, a low fixed rate interest on a 30 year mortgage does not cause home prices to go up. That being said, it is not unreasonable to anticipate lower home prices as interest rates go up because, simply put, the regression line slopes down.
One area of the scatter-plot to highlight is the data point that is closest to the upper left-hand corner of the plot, in which prices are at all-time historical highs and rates are at all-time historical lows. This point is from 08/01/2016.
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