Chapter 3.2, Problem 67E

(a)

To determine

To make: a scatterplot of the given data

Answer to Problem 67E

  

Explanation of Solution

Given:

Percent return	74	66	81	52	73	62	52	45	62	46	60	46	38
New adults	5	6	8	11	12	15	16	17	18	18	19	20	20

Calculation:

We put percent return (the explanatory variable) on the horizontal axis and new adults (the response variable) on the vertical axis.

The below figure is the scatter plot for the given data.

  

From the scatter plot. Point A and B are identified as outliers. Point A is the outlier in the X direction of the scatterplot.

Conclusion:

Thus, the required scatterplot is drawn.

(b)

To determine

To find: the point which is more influential for the regression line.

Answer to Problem 67E

Point A is more influential because the least-squares regression line deviates more strongly from the line with the original points where A is included.

Explanation of Solution

Calculation:

The below figure shows the results of removing each of these points on the correlation and regression line. The graph adds two more regression lines, one calculated after adding point A and other adding after point B . It is seen that adding the point A moves the line quite a bit. Because of point A's extreme position on the percent scale, this point has a strong influence on the position of the regression line. Point A is the outlier in the X direction of the scatterplot However, adding point B has little effect on the regression line.

  

Conclusion:

Thus, point A is more influential.