Chapter 9, Problem 12E

(a)

To determine

To explain in what way is the point unusual and does it have high leverage, a large residual or both and do you think that point is an influential point and if that point were removed would the correlation become stronger or weaker and also if that point were removed would the slope of the regression line increase or decrease, for the scatterplot (a) given in the question.

Answer to Problem 12E

It does have influential point and correlation would become stronger and slope would become stronger.

Explanation of Solution

Each of the four scatterplots given in the question that follow shows a cluster of points and one stray point. Now, by looking at the (a) scatterplot, we can say that it has a high leverage and it makes large residual smaller. And it does have an influential point. Now, if that point were removed than correlation would become stronger and increase because scatter would decrease. And also if that point were removed then the slope would become stronger and increase because the outlier pulls the line towards zero.

(b)

To determine

To explain in what way is the point unusual and does it have high leverage, a large residual or both and do you think that point is an influential point and if that point were removed would the correlation become stronger or weaker and also if that point were removed would the slope of the regression line increase or decrease, for the scatterplot (b) given in the question.

Answer to Problem 12E

It does have an influential point and correlation would weaken and slope would decrease.

Explanation of Solution

Each of the four scatterplots given in the question that follow shows a cluster of points and one stray point. Now, by looking at the (b) scatterplot, we can say that it has a high leverage and small residual. Moreover, it has an influential point. And if that point were removed than the correlation would weaken since the outlier has high $z_x\text{ and }{z}_y$ values, increasing correlation. And also if that point were removed than the slope would decrease since the outlier pulls the line from a nearly flat position to a positive slope.

(c)

To determine

To explain in what way is the point unusual and does it have high leverage, a large residual or both and do you think that point is an influential point and if that point were removed would the correlation become stronger or weaker and also if that point were removed would the slope of the regression line increase or decrease, for the scatterplot (c) given in the question.

Answer to Problem 12E

It does not have influential point and correlation would become stronger and slope would decrease slightly.

Explanation of Solution

Each of the four scatterplots given in the question that follow shows a cluster of points and one stray point. Now, by looking at the (c) scatterplot, we can say that it has little leverage and large residual. Also, no, it does not have an influential point. And if that point were removed than correlation would become stronger since scatter would decrease. And also if that point were removed than slope would remain the same and there might be slight decrease.

(d)

To determine

To explain in what way is the point unusual and does it have high leverage, a large residual or both and do you think that point is an influential point and if that point were removed would the correlation become stronger or weaker and also if that point were removed would the slope of the regression line increase or decrease, for the scatterplot (d) given in the question.

Answer to Problem 12E

It does not have influential point and correlation would become weaker and slope would remain the same.

Explanation of Solution

Each of the four scatterplots given in the question that follow shows a cluster of points and one stray point. Now, by looking at the (d) scatterplot, we can say that it has high leverage and small residual. And no, it does not have an influential point. And if that point were removed than correlation would become weaker and less negative because outlier has a large negative $z_x\times z_y$ values and in this case the slope would remain about the same since the outlier is consistent with the slope determined by the other points.