Example 13

EXAMPLE 13 Calculating and interpreting $s$ , the standard error of the estimate

Calculate and interpret the standard error of the estimate $s$ for the memory score data.

Solution

$SSE = 12$ and $n = 10$ , so

$s = \sqrt{\frac{SSE}{n - 2}} = \sqrt{\frac{12}{8}} \approx 1.2247$

Thus, the typical error in prediction is 1.2247 points. In other words, if we know the amount of time $(x)$ a given student spent memorizing, then our estimate of the student’s score on the short-term memory test will typically differ from the student’s actual score by only 1.2247 points.

Note: Here, we are rounding $s = 1.2247$ for reporting purposes. However, when we use $s$ for calculating other quantities later, we will not round until the last calculation.

NOW YOU CAN DO

Exercises 11b–22b.