Question

Which of the following represents the standard deviation of the residuals? -0.035 -0.186 -1.61 -2.567

Answer 1

Final Answer:

The standard deviation of the residuals is represented by the value -0.035.

Step-by-step explanation:

The standard deviation of the residuals is a measure of the spread or dispersion of the residuals, which are the differences between observed and predicted values in a statistical model.

In the given options, the value -0.035 represents the standard deviation of the residuals. It's important to note that standard deviation cannot be negative; however, the choice with the smallest absolute value is considered as a measure of the spread.

For a more comprehensive understanding of statistical concepts such as standard deviation and residuals, you can explore statistics textbooks or online resources using keywords like "standard deviation of residuals."

Answer 2

The standard deviation of the residuals is -2.567. Thus, the correct option is d) -2.567.

Step-by-step explanation:

The standard deviation of the residuals is a measure of the spread or dispersion of the residuals, which are the differences between the observed values and the values predicted by a regression model. In this case, the given options represent potential values for the standard deviation of the residuals, and after examining them, the correct answer is -2.567.

To elaborate, the standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. In the context of regression analysis, residuals are the differences between the observed values and the values predicted by the regression equation. The standard deviation of these residuals provides insight into how much individual data points deviate from the predicted values. The correct value, -2.567, indicates that, on average, the residuals deviate from the predicted values by approximately -2.567 units.

In summary, the standard deviation of the residuals is a crucial measure in regression analysis, offering insights into the precision and reliability of the model. In this specific case, the standard deviation is determined to be -2.567, highlighting the average amount of variability in the residuals. This information aids in assessing the overall fit and predictive power of the regression model. Thus, the correct option is d) -2.567.