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If this is the case, this would be similar to plotting the residuals (or another diagnostic quantity) against time. The index plot is a helpful diagnostic test for normal linear and particularly generalized linear models. Both outliers and influential points can be detected by the index plot. It is particularly useful when the data is in time order so that pattern in the residuals, etc. over time can be detected. If a residual index plot is showing a trend in time, then they are not independent (violation of a major assumption of linear regression).
Standard deviation plots are typically used in conjunction with mean plots. The mean plot would be used to check for shifts in location while the standard deviation plot would be used to check for shifts in scale. This sample standard deviation plot shows. 1  there is a shift in variation;  greatest variation is during the summer months.