Load the correlation by eye applet. (a) In the lower-left...

Load the correlation by eye applet. (a) In the lower-left corner of the applet, add 10 points that line up with a positive slope so that the linear correlation between the points is about $0.8 .$ Click "show $\mathbf{r}^{n}$ to show the correlation. (b) Add another point in the upper-right corner of the applet that roughly lines up with the 10 points you have in the lower-left corner. Comment on how the linear correlation coefficient changes. (c) Drag the point in the upper-right corner straight down. Take note of the change in the linear correlation coefficient. Notice how a single point can have a substantial impact on the linear correlation coefficient.

Load the correlation by eye applet.
(a) In the lower-left corner of the applet, add 10 points that line up with a positive slope so that the linear correlation between the points is about $0.8 .$ Click "show $\mathbf{r}^{n}$ to show the correlation.
(b) Add another point in the upper-right corner of the applet that roughly lines up with the 10 points you have in the lower-left corner. Comment on how the linear correlation coefficient changes.
(c) Drag the point in the upper-right corner straight down. Take note of the change in the linear correlation coefficient. Notice how a single point can have a substantial impact on the linear correlation coefficient.

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Key Concepts

Outlier Influence

Outlier influence refers to the effect that a single atypical data point can have on statistical measures, such as the linear correlation coefficient. Even one point that deviates from the overall trend can substantially alter the perceived strength and direction of a relationship, highlighting the importance of investigating and understanding such influential observations in data analysis.

Scatterplot

A scatterplot is a graphical representation of data in which individual data points are plotted on a two-dimensional coordinate system. It is a foundational tool in statistical analysis, allowing one to visually assess the relationship between two variables and identify patterns such as clusters, trends, and potential outliers.

Linear Correlation Coefficient

This is a measure of the strength and direction of the linear relationship between two variables. It quantifies how closely data points in a scatterplot cluster around a straight line, with values ranging from -1 to 1. A value close to 1 indicates a strong positive linear relationship, while a value near -1 indicates a strong negative linear relationship.

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