Q.4.163 - Elementary Statistics

Question

Shortleaf Pines. The data from Exercise 4.80 for volume, in cubic feet, and diameter at breast height, in inches, for $70$ shortleaf pines are on the WeissStats site.

1. Decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate. If so, then also do parts $\left(b\right)$ and $\left(c\right)$.
2. obtain the linear correlation coefficient 
3. interpret the value of $r$ in terms of the linear relationship between the two variables in question.

Step-by-Step Solution

Answer

The concave upward curving pattern may be seen in the data. As a result, there is no linear pattern in the data. So we can omit the portions (b) and (c)

Part (a) Step 1: Given Information

 The data from Exercise 4.80 for volume, in cubic feet, and diameter at breast height, in inches, for $70$ shortleaf pines are on the WeissStats site.

Part (a) Step 2: Explanation

The MINITAB: can be used to create a scatterplot for the given data.

Step 1: Select Graph > Scatterplot from the drop-down menu.

Step 2: Click OK after selecting With Connect Line.

Step 3: Add a VOLUME column to the $Y$ variables section.

Step 4: Add a DIAMETER column to the $X$ variables section.

Step 5: Click the OK button.

The resulting scatterplot will be

Finding a regression line for the data is not acceptable since the observations are not dispersed around a line in the scatterplot above.