Chapter 9, Problem 11E

(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 11E

It does not have influential point and correlation would increase and slope does not change much.

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 is of small residual. And it does not have an influential point or not influential for the slope. Now, if that point were removed than correlation would decrease because outlier has large $z_x\text{ and }{z}_y$ , increasing correlation. And also if that point were removed then the slope would not change much because the outlier is in line with other points.

(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 11E

It does have an influential point and correlation would weaken and slope will move toward zero.

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 and will increase towards zero. And also if that point were removed than the slope would increase towards zero since outlier makes it negative.

(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 11E

It does have influential point and correlation would increase and slope would increase 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 some leverage and large residual. Also, yes, it has an influential point. And if that point were removed than correlation would increase since scatter would decrease. And also if that point were removed than slope would increase slightly since the scatter would 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 11E

It does not have influential point and correlation would become stronger and slope would change very little.

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 little leverage and large residual. And no, it does not have an influential point. And if that point were removed than correlation would increase since scatter would decrease and in this case the slope would change very little as scatter would decrease.