An Illustration

Figure 9-1 is a simple illustration using a single proxy to predict temperature. Plotted are 100 pairs of points that may be thought of as a hypothetical annual series of proxy data and corresponding instrumental surface temperature measurements over a 100-year calibration period. The solid black line is the linear fit to these data, or the calibration, which forms the basis for predictions of temperatures during other time periods. Here the prediction of temperature based on a proxy with value A is TA and the proxy with value B predicts the temperature TB.

The curved blue lines in Figure 9-1 present the calibration error, or the uncertainty in predictions based on the calibration (technically the 95 percent prediction interval, which has probability 0.95 of covering the unknown temperature), which is a standard component of a regression analysis. In this illustration, the uncertainty associated with temperature predictions based on proxy data is greater at point A than it is at point B. This is because the calibration errors are magnified for predictions based on proxy

FIGURE 9-1 An illustration of using linear regression to predict temperature from proxy values. Plotted are 100 pairs of points corresponding to a hypothetical dataset of proxy observations and temperature measurements. The solid black line is the least-squares fitted line and the blue lines indicate 95 percent prediction intervals for temperature using this linear relationship. The dashed line and the red line indicate possible departures from a linear relationship between the proxy data and the temperature data. The figure also illustrates predictions made at proxy values A and B and the corresponding prediction intervals (wide blue lines) for the temperature.



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