Which of the following is true regarding the standard error of the estimate ($\mathrm{SE}$)?

• A. It is calculated by dividing the sum of the residuals ($\sum e$) by the number of observations ($n$).
• B. It increases as the sample size ($n$) increases, assuming variance stays constant.
• C. It measures the typical distance that observed values fall from the regression line.
• D. It is always equal to the standard deviation of the independent variable ($s_x$).

Answer: (C)

Verified step by step guidance

1. Understand that the standard error of the estimate (SEE) is a measure used in regression analysis to quantify the typical distance between observed data points and the predicted values on the regression line.
2. Recall that the SEE is related to the residuals, which are the differences between observed values and predicted values, but it is not simply the sum of residuals divided by the number of observations.
3. Recognize that the SEE is calculated using the formula: \(\text{SEE} = \sqrt{\frac{\sum (y_i - \hat{y}_i)^2}{n - 2}}\), where \(y_i\) are observed values, \(\hat{y}_i\) are predicted values, and \(n\) is the number of observations.
4. Note that the SEE tends to decrease as the sample size increases if the variance remains constant, because the estimate of the regression line becomes more precise with more data.
5. Understand that the SEE is not equal to the standard deviation of the independent variable; instead, it relates to the variability of the dependent variable around the regression line.