Q.4.71 - Elementary Statistics

Question

U.S Presidents. The Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeisStats site for those presidents who are not still living at the time of this writing.

a. Obtain the scatterplot for the data

b. Decide whether finding a regression line for the data is reasonable. if so, then also do parts (c)-(f) 

c. Determine and interpret the regression equation for the data

d.Identify the potential outliers and influential observation 

e. In case a potential outlier is present, remove it and discuss the effect.

f. In case potential  influential observations is present,remove it and discuss the effect. 

Step-by-Step Solution

Answer

(a) 

(b) Yes, it is reasonable

(c)  The regression equation for the data is $\hat{y}=5.3679+1.1848x$

(d) There is no potential outliers and influential observation .

(e) Not applicable

(f) Not applicable 

Part(a) Step 1: Given Information

Given in the question that the Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeisStats site for those presidents who are not still living at the time of this writing .  we have to obtain the scatterplot for the data. 

Part(a) Step 2: Explanation

Part(b) Step 1: Given Information

Given in the question that the Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeisStats site for those presidents who are not still living at the time of this writing .  we have to decide whether finding a regression line for the data is reasonable. 

Part(b) Step 2: Explanation

If the scatterplot has no strong curvature, it is reasonable to find the regression line for the data.

Because the scatterplot has no strong curvature, it is reasonable to identify the regression line to the data. The graph shows left to right upward trend 

Part(c) Step 1: Given Information

Given in the question that the Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeisStats site for those presidents who are not still living at the time of this writing .  we have to determine and interpret the regression equation for the data. 

Part(c) Step 2: Explanation

Formula used to find the regression equation is 

$\hat{y}=b_0+b_{1}x$

where,

$b_0=5.3679$

$b_1=1.1848$

therefore,

$\hat{y}=5.3679+1.1848x$

Part(d) Step 1: Given Information

Given in the question that the Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeisStats site for those presidents who are not still living at the time of this writing .  we have to  identify the potential outliers and influential observation .

Part(d) Step 2: Explanation

An outlier is a data point that is far off the regression line.

An influential observation is one where the removal of a point causes a significant change in the regression equation. That instance, removing a point causes a significant shift in the regression line's direction.

There are no potential outliers in the dataset because all of the points are closed to the regression line in the plotted graph. There is no considerable change in the direction of the regression line when a point is removed, hence there are no potentially influencing observations. 

Part(e) Step 1: Given Information

Given in the question that the Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeisStats site for those presidents who are not still living at the time of this writing .  we have to obtain  in case a potential outlier is present, remove it and discuss the effect. 

Part(e) Step 2: Explanation

There are no outliers in part d so this is not applicable. 

Part(f) Step 1: Given Information

Given in the question that the Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeisStats site for those presidents who are not still living at the time of this writing .  we have to obtain  in case potential  influential observations is present,remove it and discuss the effect.  

Part(f) Step 2: Explanation

There is no  potential influential observation in part d. so this is not applicable.