Fertility in Japan: curve-fitting the total fertility rate

This is a subsidiary page to the fertility in Japan page that discusses different models to explain the total fertility rate data in Japan (1947-200. We draw on Human Fertility Database data (data downloaded on December 2, 2013, last updated August 8, 2012). The data collected by the Human Fertility Database is based on government data collection by the government of Japan. Details about the modalities of data collection are available here.

Raw time series data

Linear model

Single straight line fit

Denote by $t$ the year. Then, the best linear fit predicting the total fertility rate in year $t$ is:

$-0.032306t+65.87150$

Quick summary information about the goodness of fit is below (paste from R data, needs to be converted to table):

Residuals:
     Min       1Q   Median       3Q      Max 
-0.77971 -0.19170 -0.02246  0.08087  1.59348 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 65.871500   6.016802   10.95 4.98e-16 ***
yearrange   -0.032306   0.003042  -10.62 1.69e-15 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.439 on 61 degrees of freedom
Multiple R-squared:  0.649,     Adjusted R-squared:  0.6433 
F-statistic: 112.8 on 1 and 61 DF,  p-value: 1.693e-15

Piecewise linear models