Chapter 3.1, Problem 25E

To determine

To find: what is responsible for the effect of correlation.

Answer to Problem 25E

In scatterplot that all points are in line except (5, 1), this is an outlier. The remaining 5 points are more tightly clustered in a straight line.

Explanation of Solution

Given:

x	1	2	3	4	10	10
y	1	3	3	5	1	11

  

We assume that $X$ will help explain $Y$ . So $X$ is the explanatory and $Y$ is the response variable. We want to see $Y$ changes when $X$ changes, so we put $X$ (the explanatoryvariable) on the horizontal axis and $Y$ (the response variable) on the vertical axis. From the above scatter plot we observe that, the overall pattern moves from lower left to upper right. We call this a positive association between the two variables. The form of the relationship is liner. That is, the overall pattern follows as straight line from lower left to upper right. The correlation of 0.5 shows there is a moderately strong, positive linear relationship between $X$ and $Y$ . We can clearly see in scatterplot that all points are in line except (5, 1), this is an outlier. This point is responsible for reducing the correlation despite a strong straight - line relationship. Removing the outlier would definitely increase the correlation since remaining 5 points are more tightly clustered in a straight line.