Regression Analysis: Understanding Standard Deviation of Residuals

What does the standard deviation of the residuals represent in regression analysis?

Options:

a) -0.035

b) -0.186

c) -1.61

d) -2.567

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.

Final Answer:

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

In regression analysis, the standard deviation of the residuals plays a significant role in assessing the accuracy and reliability of the regression model. It measures how spread out the residuals are, indicating the variability or dispersion of the data points around the regression line.

The correct option for the standard deviation of the residuals is -2.567, which highlights the amount of deviation between the observed values and the predicted values by the regression model. This value signifies the average amount of variability in the residuals, with larger deviations indicating less precise predictions.

Understanding the standard deviation of the residuals is crucial for evaluating the overall fit of the regression model and determining the effectiveness of the predictions. It provides insights into the extent of variation in the data points and helps in assessing the model's accuracy in capturing the relationships between variables.