Question

Plot the points and determine whether the data have positive, negative, or no linear correlation (see figures below). Then use a graphing utility to find the value of $r$ and confirm your result. The number $r$ is called the correlation coefficient. It is a measure of how well the model fits the data. Correlation coefficients vary between $-1$ and 1, and the closer $|r|$ is to 1, the better the model. $$(1,36),(2,10),(3,0),(4,4),(5,16),(6,36)$$

Short answer

The given points do not show any strong positive or negative correlation when plotted on a graph. The correlation coefficient $r$ will likely result in a value closer to zero.

Step-by-step solution

Plotting the Points

Begin by plotting the six given points on a graph. The points are (1,36), (2,10), (3,0), (4,4), (5,16), (6,36). Observe the pattern or trend after plotting all the points.

Checking for Correlation

Once the points are plotted, check if there seems to be any correlation. Since the points do not follow a straight line path in either upward or downward slope, there doesn't appear to be a linear correlation.

Calculating the Correlation Coefficient

Despite the visual interpretation, let's use the Pearson correlation coefficient formula or a graphing utility to calculate the correlation coefficient $r$.

Confirming the Result

The correlation coefficient will likely be closer to zero rather than -1 or 1, confirming the interpretation from step 2 that there is no strong linear correlation among the given data.