Consider the data set below. $$\begin{array} { | l l |l l |}
\hline x & 1 & 2 & 3 \
\hline y & 7 & 6 & 5
\end{array}$$ Adding the data point (3, 6) to this data set:
A) changes the correlation.
B) changes the slope of the regression line.
C) Both A and B are correct.
D) Neither A nor B is correct.

Question

Consider the data set below. $$\begin{array} { | l  l |l  l |} 
\hline x & 1 & 2 & 3 \
\hline y & 7 & 6 & 5
\end{array}$$ Adding the data point (3, 6) to this data set:
A) changes the correlation.
B) changes the slope of the regression line.
C) Both A and B are correct.
D) Neither A nor B is correct.

Quizplus · Accepted Answer

Adding the data point (3, 6) changes both the correlation and the slope of the regression line. The original data set shows a perfect negative linear relationship with a correlation of -1. Adding the point (3, 6) disrupts this perfect relationship, thereby changing the correlation. Since the correlation is directly related to the slope of the regression line (in the sense that a change in correlation implies a change in the direction or strength of the linear relationship), the slope of the regression line will also change.

Consider the Data Set Below x123y765\begin{array} { | l l |l l |} \hline x & 1 & 2 & 3 \\\hline y & 7 & 6 & 5\end{array}xy​17​26​35​​

Consider the Data Set Below $\begin{array} { | l l |l l |} \hline x & 1 & 2 & 3 \\\hline y & 7 & 6 & 5\end{array}$