Question

Draw two scatterplots, one for which \(r=1\) and a second for which \(r=-1\).

Short answer

Generated two scatterplots. The first scatterplot shows a perfect positive linear correlation with \(r=1\) which can be seen as all points fall on an upward sloping line. The second scatterplot demonstrates a perfect negative linear correlation with \(r=-1\) as all points lie along a downward sloping line.

Step-by-step solution

Create Positive Correlation Scatterplot

The easiest way to create a scatterplot with \(r=1\) is by plotting points that fall exactly on a single line. This can be done using a set of ordered pairs with an equal interval between the x and y coordinates. For simplicity, use five ordered pairs such as \((1,1)\), \((2,2)\), \((3,3)\), \((4,4)\), \((5,5)\). Plot these on the x-y graph.

Create Negative Correlation Scatterplot

To create a scatterplot with \(r=-1\), plot points that also fall exactly on a single line, but this time with a negative slope. It can be achieved by plotting pairs with a consistent interval between the x coordinate and a decreasing y coordinate. For simplicity, five ordered pairs such as \((1,5)\), \((2,4)\), \((3,3)\), \((4,2)\), \((5,1)\) could be used. Plot these on the x-y graph.