Q. 4.164 - Elementary Statistics

Question

The data from Exercise $4.114$ for age and percentage of body fat for 18 randomly selected adults are on the Weiss Stats site.

a. Decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate, If so, then also parts $\left(b\right)$ and $\left(c\right)$

b. Obtain the linear correlation coefficient.

c. Interpret the value of $r$ in terms of the linear relationship between the two variables in question.

Step-by-Step Solution

Answer

(a) As a descriptive metric for the data, the linear correlation coefficient is acceptable.

(b) The linear correlation coefficient is $0.792$.

(c) It suggests that the variables age and $\%$ fat have a significant positive linear connection.

Part (a) Step: 1 Given Information

Whether the use of linear correlation coefficient is appropriate or not.

Part (a) Step 2: Explanation

The scatterplot for the given data can be drawn by using the MINITAB:

Step 1: Choose Graph $>$Scatterplot.

Step 2: Choose With Connect Line, and then click OK.

Step 3: Under$Y$ variables, enter a column of$\%$ FAT.

Step 4: Under $X$ variables, enter a column of AGE.

Step 5: Click OK.

Part (a) Step 3: Explanation

The scatterplot obtained will be,

Because the observations are spread around a line in the scatterplot above, it is fair to establish a regression line for the data.

Part (b) Step 1: Given Information

The linear correlation coefficient.

Part (b) Step 2: Explanation

The linear correlation coefficient can be obtained by using MINITAB as follows:

Step 1: Choose Stat >Basic Statistics>Correlation

Step 2: In Variables, select$\%$ FAT and $\%$FAT from the box on the left

Step 3: Click OK.

The MINITAB output will be:

Hence, the linear correlation coefficient will be $0.792$.

Part (c) Step 1: Given Information

The interpretation of the value of linear correlation coefficient.

Part (c) Step 2: Explanation

The linear correlation coefficient will be $0.792$ which is close to $1.$ 

It suggests that the variables age and $\%$ fat have a significant positive linear connection.

If the value of $x$ increases, then the corresponding value of $y$ increases.

In other words, the smaller value of $x$ is related with the smaller value of $y$ or the larger value of $x$is related to the larger value of $y.$