i worked on the following tests and plots:
1.Standardized Residual Plot:
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- This plot displays the standardized residuals of the model over time.
- Residuals are the differences between observed and predicted values.
- Ideally, residuals should fluctuate randomly around zero, without any discernible pattern.
- In our plot, we observed a fairly random scatter of residuals, although there are some instances of potential outliers.
- Histogram and Estimated Density Plot:
- The histogram bins the standardized residuals to show their distribution.
- An overlaid kernel density estimate (KDE) shows a smoothed version of this distribution.
- A standard normal distribution (N(0,1)) is plotted for comparison.
- A good-fitting model would have residuals that closely follow a normal distribution. The histogram should resemble the bell shape of the normal distribution curve.
- Normal Q-Q Plot:
- The quantile-quantile plot compares the quantiles of the residuals with the quantiles of a normal distribution.
- If the residuals are normally distributed, the points should fall approximately along the red line.
- In the plot, the points largely follow the line, suggesting normality, but deviations at the ends may indicate heavier tails than the normal distribution.
- Correlogram (ACF Plot):
- The correlogram, or autocorrelation function plot, shows the correlation of the residuals with themselves at different lags.
- We look for correlations that are significantly different from zero at various lag intervals.
- In a well-fitted model, we expect that there will be no significant autocorrelation in the residuals. Here, most autocorrelations are within the confidence band, indicating no significant autocorrelation.