Post 1 Linear regression analysis

Post 2 Hypothesis testing of temperature trends

Post 3 Confidence intervals around temperature trend lines

Post 4 Statistical power of temperature trends

Post 5

**Piecewise linear regression applied to temperature trends**

The posts are gathered in this pdf document.

Start of post 5

**Piecewise linear regression applied to temperature trends**

The temperature trend line from December 2000 to December 2013 is flat, while the one from January 1984 to November 2000 increases with 0.22°C/decade, as shown with the two blue lines in Figure 5.1.

Figure 5.1: Monthly temperatures in the last 30 years with trend lines |

This leads many contrarians to argue that the increasing temperature trend before the turn of the millennium is followed by a flat trend, and they often illustrate their claim with the red schematic line in Figure 5.1. The red line is, however, not based on calculations, and it does not match the monthly temperatures that it claims to represent. The two blue lines are calculated with linear regression analysis, and they represent the temperatures in their segments when the segments are evaluated isolated from each other. But the trend lines are not continuous at the breakpoint between November and December 2000, and they therefore do not represent the trend for the whole time period in Figure 5.1.

We may calculate a piecewise linear trend line that is continuous at the breakpoint. This new trend line is a “best fit” to the temperatures in the whole time period, just as the two blue lines are the best fits for their time periods. The new trend line has an increasing trend also after the turn of the millennium, as the green line in Figure 5.1 shows. It is calculated with piecewise linear regression analysis.