Examples of residuals in the following topics:
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- Observations below the line have negative residuals.
- The observation marked by an " has a small, negative residual of about -1; the observation marked by "+" has a large residual of about +7; and the observation marked by "$\Delta$" has a moderate residual of about -4.
- The residuals are plotted at their original horizontal locations but with the vertical coordinate as the residual.
- For instance, the point (85.0, 98.6)+ had a residual of 7.45, so in the residual plot it is placed at (85.0, 7.45).
- The second data set shows a pattern in the residuals.
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- Note that the sum of the residuals within a random sample is necessarily zero, and thus the residuals are necessarily not independent.
- To create a residual plot, we simply plot an $x$-value and a residual value.
- The average of the residuals is always equal to zero; therefore, the standard deviation of the residuals is equal to the RMS error of the regression line.
- Residual plots can allow some aspects of data to be seen more easily.
- Differentiate between scatter and residual plots, and between errors and residuals
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- 8.11: Nearly normal residuals: The normal probability plot shows a nearly normal distribution of the residuals, however, there are some minor irregularities at the tails.
- Constant variability of residuals: The scatter-plot of the residuals versus the fitted values does not show any overall structure.
- In addition, the residuals do appear to have constant variability between the two parity and smoking status groups, though these items are relatively minor.
- Independent residuals: The scatterplot of residuals versus the order of data collection shows a random scatter, suggesting that there is no apparent structures related to the order the data were collected.
- The rest of the residuals do appear to be randomly distributed around 0.
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- A normal probability plot of the residuals is shown in Figure 8.9.
- In a normal probability plot for residuals, we tend to be most worried about residuals that appear to be outliers, since these indicate long tails in the distribution of residuals.
- We consider a plot of the residuals against the cond new variable and the residuals against the wheels variable.
- There appears to be curvature in the residuals, indicating the relationship is probably not linear.
- We see some slight bowing in the residuals against the wheels variable.
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- Mathematically, we want a line that has small residuals.
- Perhaps our criterion could minimize the sum of the residual magnitudes:
- However, a more common practice is to choose the line that minimizes the sum of the squared residuals:
- In many applications, a residual twice as large as another residual is more than twice as bad.
- Squaring the residuals accounts for this discrepancy.
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- The Residual Dividend Model first uses earnings to finance new projects, then distributes the remainder as dividends.
- The Residual Dividend Model is a method a company uses to determine the dividend it will pay to its shareholders.
- The Residual Dividend Model is an outgrowth of The Modigliani and Miller Theory that posits that dividends are irrelevant to investors.
- The Residual Model dividend policy is a passive one and, in theory, does not influence market price because the same wealth is created for the investor regardless of the dividend.
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- These differences are referred to as residuals, and they can be standardized and adjusted to follow a normal distribution with mean $0$ and standard deviation $1$.
- The adjusted standardized residuals, $d_{ij}$, are given by:
- Subclavian site/no infectious complication has the largest residual at 6.2.
- As these residuals follow a Normal distribution with mean 0 and standard deviation 1, all absolute values over 2 are significant.
- The association between femoral site/no infectious complication is also significant, but because the residual is negative, there are fewer individuals than expected in this cell.
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- The most commonly used measure of distance is the studentized residual.
- Observation B has small leverage and a relatively small residual.
- Observation C has small leverage and a relatively high residual.
- Observation D has the lowest leverage and the second highest residual.
- Observation E has by far the largest leverage and the largest residual.
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- In metalloproteins, metal ions are usually coordinated by nitrogen, oxygen, or sulfur centers belonging to amino acid residues of the protein.
- These donor groups are often provided by side-chains on the amino acid residues.
- Given the diversity of metalloproteins, virtually all amino acid residues have been shown to bind metal centers.
- In addition to donor groups that are provided by amino acid residues, a large number of organic cofactors function as ligands.
- The three coordinating histidine residues are shown in green, hydroxide in red and white, and the zinc in gray.
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- 8.11: Nearly normal residuals: The normal probability plot shows a nearly normal distribution of the residuals, however, there are some minor irregularities at the tails.
- Constant variability of residuals: The scatter-plot of the residuals versus the fitted values does not show any overall structure.
- In addition, the residuals do appear to have constant variability between the two parity and smoking status groups, though these items are relatively minor.
- Independent residuals: The scatterplot of residuals versus the order of data collection shows a random scatter, suggesting that there is no apparent structures related to the order the data were collected.
- The rest of the residuals do appear to be randomly distributed around 0.