Consider the scatter diagrams. A data point with an extreme x value can heavily
ID: 3053799 • Letter: C
Question
Consider the scatter diagrams. A data point with an extreme x value can heavily influence the position of the least-squares line. Answer the following questions for each diagram:
(a) Is there an influential point?
(b) If you remove the influential point, will the slope of the new least-squares line be larger or smaller than the slope of the line from the original data? (you don’t need to calculate anything, just visually estimate the slope)
(c) Will the correlation coefficient r be larger or smaller?
Figure 2 Figure 1 Scatter Diagram Scatter Diagram ? 14- 10 15 10 0 2 46 8 10 12 14 16 0 2 46 8 10 1 14Explanation / Answer
a) An influential point is an outlier that greatly affects the slope of the regression line.
yes. there is an influential point.
b) If we remove the influential point, the slope of the new least-squares line will be larger than the slope of the line from the original data.
for this we will make the regression line first with the influential point and then without it. and compare the slope.
c) Sometimes, an influential point will cause the correlation coefficient to be bigger; sometimes, smaller.
In figure 1 the correlation coefficient r is smaller with the outlier than without it.
In figure 2 the correlation coefficient r is bigger with the outlier than without it.