Question

Exercis4.163

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.

a. construct a scatterplot for the data.

b. decide whether using the rank correlation coefficient is reasonable.

c. decide whether using the linear correlation coefficient is reasonable.

d. find and interpret the rank correlation coefficient.

Short answer

(a)

(b) The rank correlation is reasonable.

(c) The linear correlation coefficient is not reasonable.

(d) The rank correlation coefficient has a value of $0.988$. It shows that the variables rankdiameter and rankvolume have a strong positive linear connection.

Step-by-step solution

Part (a)Step 1: Given information

Given in the question that , From exercise 4.163

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.

We need to construct a scatterplot for the data.

Part(a) Step 2: Explanation

Pines, shortleaf The WeissStats site has data from Exercise 4.80 for volume in cubic feet and diameter at breastheight in inches for 70 shortleaf trees.

Calculation:

Procedure for MINITAB:

Using MINITAB, create a scatterplot for the supplied data.

Given information:

Step 1: Select Scatterplot > Graph.

Step 2: Click OK after selecting With Connect Line.

Step 3: Create a Volume column under Y variables.

Step 4: Create a Diameter column under X variables.

Step 5: Click the OK button.

OUTPUT FROM MINITAB:

It is clear from the graph that time and score have a negative linear connection.

Part(b) Step 1: Given information

Given in the question that , From exercise 4.163

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.

We need to decide that whether the use of rank correlation coefficient is reasonable.

Part (b) Step 2: Explanation

Because the variable diameter grows as the variable volume increases, the rank correlation coefficient is reasonable. That is, smaller diameter values are associated to smaller volume values, and bigger diameter values are related to larger volume values.

Part(c) Step 1: Given information

Given in the question that , From exercise 4.163

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.

We need to decide that whether the use of linear correlation coefficient is reasonable.

Part(c) Step 2: Explanation

Because there is a convex upward curved pattern, and the variable diameter rises as the variable volume increases, utilising the linear correlation coefficient is not logical. As a result, the data does not appear to represent a linear pattern.

Part(d) Step 1: Given information

Given in the question that , From exercise 4.163

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.

We need to find and interpret the rank correlation coefficient.

Part(d) Step 2: Explanation

Using MINITAB, find the rank for diameter and volume first.

Step 1: Select Data >Rank in the MINITAB method.

Step 2: Select Diameter in Rank data in.

Step 3: Select Rank diameter from the Store Ranks in menu.

Step 4: Select Volume in Rank data in.

Step 5: Select Rank volume from the Store Ranks in menu.

Correlation:

Procedure for MINITAB:

Step 1: Choose Stat >Basic Statistics > Correlation from the drop-down menu.

Step 2: Select Rank diameter and Rank volume from the left-hand box in Variables.

Step 3: Press the OK button.

OUTPUT FROM MINITAB:

Rank diameter and Rank Volume are related.

Pearson correlation of Rank Diameter and Rank Volume$=0.988$

$P-\text{Value}=0.000$

$=0.988$

The rank correlation coefficient obtained from MINITAB is $0.988$.

Interpretation: The rank correlation coefficient has a value of $0.988$. It shows that the variables rank diameter and rank volume have a strong positive linear connection.