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Linear regression is commonly used for predictive analysis and modeling.

Set the horizontal axis for HbA (the explanatory variable) and the vertical axis for FPG (the response variable).

The scatterplot for the supplied data is presented below using the MINITAB:

The general pattern moves from the bottom left to the higher right, as shown in the graph. That is, people with a higher HbA have a higher FPG. This is referred to as a positive relationship between the two variables. The relationship is linear in nature. That example, the general pattern runs from bottom left to higher right in a straight line. Because the points deviate greatly from the line and there are some outliers, the relationship is weak. Therefore, the required scatterplot is drawn.

The correlation $r$ with all $18$ individuals using the MINITAB is $r=0.482$

Without subject $15$ the correlation coefficient is $r=0.568$

Without subject $18$ the correlation coefficient is$r=0.384$

Without subject $15$ and without subject $18$ the correlation is $r=0.324$

The Correlation increases by $0.086$ after outlier subject $15$ is removed. However, removing subject $15$ from the equation has no influence on the association. Because of subject $15\text{'}s$ extreme position on the HbA scale, the position of the regression line is strongly influenced by this point. The Correlation drops by $0.098$ when the outlier subject$18$ is removed. One outlier can be wholly responsible for a high correlation value that would otherwise be quite low (without the outlier). Needless to note, major decisions should never be made solely on the basis of the correlation coefficient's value (i.e., examining the respective scatterplot is always recommended). These are known as 'good' outliers. Both subjects $15$ and $18$ have an impact since the linear correlation coefficient varies dramatically when they are combined.

Therefore,

The correlation $r$ with all $18$ subjects is $r=0.482$

The correlation $r$ without subject $15$ is $r=0.568$

The correlation $r$ without subject $18$ is $r=0.384$

The least-square lines with all $18$topics, without subject $15$ and without subject $18$ are shown in the diagram below.

The relevance of subject $18$ can be shown here. This point can be considered an excellent outlier because it spreads the pattern to the top right. When this point is removed, the correlation decreases since the remaining points exhibit no discernible pattern. Because this point is so distant from the regression line, Subject $15$ has a very large residual. Least-squares lines minimize the sum of squares of the vertical distances between the points. The line is pulled toward itself by a point that is extreme in the $X$ direction and has no other points nearby. It's known as influential spots. It lowers the line's incline. Therefore, subject $15$ and subject $18$ both are influential.