Final answer:
The standard error of the estimate, denoted as se, is a measure used to quantify the accuracy of predictions in a regression analysis. It is calculated using the sum of squared errors (SSE) and the number of data points (n). When the population standard deviation is unknown, the sample standard deviation is used as an estimate, and the standard error is the standard deviation of a statistic's sampling distribution.
Step-by-step explanation:
The standard deviation of the residual, denoted as se, is more commonly referred to as the standard error of the estimate. This term describes the measure of the accuracy of predictions made with a regression line. In a regression analysis, the formula for calculating the standard error of the estimate is s = √(SSE/n-2), where SSE is the sum of the squared errors, and n is the number of data points. The standard error of the estimate provides an indication of how much the data points deviate, on average, from the actual data points.
In scenarios where we do not know the population standard deviation (σ), we use the sample standard deviation (s) as an estimate. The standard error for the hypothesis test, specifically for the difference in sample means, is calculated using the two sample standard deviations from independent samples. The formula usually involves combining the variances of the two samples and dividing by the sample sizes, then taking the square root of the result.
Sampling variability of a statistic is often measured by its standard error, which is the standard deviation of the sampling distribution of the statistic, like the sample mean. An important point to note is that the standard error of the mean is given as σ/√n, which is the population standard deviation divided by the square root of the sample size, n.