Q.2.155 - Elementary Statistics

Question

U.S. Presidents. The data from Exercise 4.71 for the ages at the inauguration and of death for the presidents of the United States are on the Weissstats site.

a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate, If so, then also do parts (b) and (c).

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 of data, we used the linear correlation coefficient.

b). The linear correlation coefficient $=0.609$.

c). The positive linear correlation coefficient indicates a somewhat favorable relationship between the inauguration and death of US presidents.

Part (a) Step 1: Given Infromation

The table below shows the ages of the presidents of the United States at their inauguration and death, as calculated using exercise  $4.71$.

Part (a) Step 2: Explanation

Draw a scatter plot for the presidents of the United States' inaugurations and deaths.

As observed in the scatter plot, the data points are distributed along a line.

As a consequence, as a data descriptive metric, we picked the linear correlation coefficient.

Part (b) Step 1: Given Information

The table below shows the ages of the presidents of the United States at their inauguration and death, as calculated using exercise $4.71$.

Part (b) Step 2: Explanation

Any technique may be used to find the correlation coefficient.

We'll begin by inputting the brides and their scores, followed by the ultimate outcome.

Hence,

The linear correlation coefficient $=0.609$.

Part (c) Step 1: Given Information

The table below shows the ages of the presidents of the United States at their inauguration and death, as calculated using exercise  $4.71$

Part (c) Step 2: Explanation

The linear correlation co-efficient $r=0.609$.

The positive linear correlation coefficient indicates a somewhat favorable relationship between the inauguration and death of US presidents.