Now we will think about how to estimate the error in a prediction when we do not have a data point to compare the prediction to. When we make a prediction, we always want to acknowledge how far the prediction is from the observed data value; this is the error. If we make a prediction and we don't have an actual data value to compare it to, then we have to estimate the error. To do this, we estimate the average amount of error in the predictions for the data overall. In other words, we estimate how far the data is from the line on average. This is the standard deviation in the errors (aka standard error), and we denote it, Se . For the previous data set, the standard deviation in the errors is se = 1.4 weeks. Circle the Se in the print-out on the previous page (The mean of the errors is zero if we don't round. This will always be true.) 2) The majority of the data should fall within one standard error of the prediction from the regression line. In other words, the majority of this data should have an error that is within (no more than) +1.4 weeks. Use the error calculations in the table on the previous page to determine the percentage of this data that falls within one standard error of the prediction from this regression line. Now we will use se to comment on the error in this prediction, and to make a prediction interval. Example: The person whose fetus's abdominal circumference is 150mm is predicted to be approximately 19.7 weeks pregnant. (AC=150mm and GAWK=19.7weeks). Since no fetus in the data set has AC=150 mm, we cannot determine the error in our prediction of 19.7 weeks. Therefore, we will use the standard error as an estimate. The error in the predicted GAWK is estimated to be + 1.4 weeks. We do not know if this error is positive or negative. In other words, we do not know if we have over- or under-estimated her GAWK. If the error is positive 1.4 weeks, then its GAWK could be up to (19.7 +1.4) = 21.1 weeks. If the error is negative, then its GAWK could be down to (19.7 - 1.4) = 18.3 weeks. In other words, taking possible error into account, we estimate that the fetus's gestational age is between 18.3 and 21.1 weeks. So, for a prediction , and a standard error Se, we have a prediction interval: Prediction Interval: [D - Se, D + Sel