Question

We can plot the residuals sequentially over time to look for correlated observations. How are violations indicated?

A. When positive residuals are shown consistently over time and negative residuals are shown consistently over time
B. When all the residuals are negative
C. When positive residuals and negative residuals alternate over a few periods, sometimes positive or negative for a couple of periods.
D. There is no detection method

Answer 1

Violations in residual independence over time are indicated by consistent patterns of positive or negative residuals. We can identify outliers on a scatter plot using standard deviations, and the correlation coefficient 'r' measures the linear relationship's strength, which can be revised after removing outliers.

Step-by-step explanation:

Violations of independence in residuals over time are indicated by patterns in the sequential plot of residuals. Option A is correct: a violation is indicated when there is a consistent display of positive residuals over time or negative residuals over time. We can visually inspect a scatter plot to identify outliers by drawing lines that are two standard deviations above and below the best-fit line. Residuals that fall outside this range are potential outliers. Furthermore, the correlation coefficient (r) can provide insights into the strength of the linear relationship and can be recalculated after removing outliers to see how the line fit improves.

When plotting points in a scatter plot, we can identify positive correlation, negative correlation, and zero correlation based on the direction and closeness of data points to a straight line. This analysis is crucial when addressing whether a linear model is appropriate or if a different model should be considered.