Q 4 .105 - Elementary Statistics

Question

a. Decide whether finding a regression line for the data is reasonable. If so, then aiso do parts (b)-(d).

b. Obrain the coefficient of determination.

c. Determine the percentage of variation in the observed values of the response variable explained by the regression. and intermret your answer.

d. State how useful the regression equation appears to be for making predictions.

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

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

Step-by-Step Solution

Answer

a) Because the observations are scattered around a line in the scatterplot above, it is reasonable to find a regression line for the data.

b)  The coefficient of determination is 0.367. 

c) It can be interpreted as the linear relationship between the inauguration $\left(x\right)$ and death $\left(y\right)$ accounts for $36.7$ percent of the variability in death.

d) The regression equation cannot be used to make predictions because the percentage of variation in the observed values of the response variable explained by the regression is less than$50$ percent. 

Part a Step 1 Given Information

The information Please A/mana provides data on the ages at the inauguration and of death for the presidents of the United States. We give those data on the WeissStats site for those presidents who are not still living at the time of this writing. 

Part a Step 2 Explanation

The scatterplot for the Provided 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 $\mathbf{Y}$ variables, enter a column of DEATH

Step 4: Under $\mathbf{X}$ variables, enter a column of INAUGRATION

Step 5: Click OK

The scatterplot obtained will be

Because the observations are scattered around a line in the scatterplot above, it is reasonable to find a regression line for the data.

Part b Step 1 Given Information

The information Please A/mana provides data on the ages at the inauguration and of death for the presidents of the United States. We give those data on the WeissStats site for those presidents who are not still living at the time of this writing. 

Part b Step 2 Explanation

The coefficient of determination can be calculated by using MINITAB as follows:

Step 1: Choose Stat >Regression >Regression

Step 2: In Response, enter the column DEATH

Step 3: In Predictors, enter the column INAUGRATION

Step 4: Click OK

The MINITAB output will be:

As a result, the coefficient of determination is 0.367.

Part c Step 1 Given Information

The information Please A/mana provides data on the ages at the inauguration and of death for the presidents of the United States. We give those data on the WeissStats site for those presidents who are not still living at the time of this writing. 

Part c Step 2 Explanation

The determination coefficient will be $0.367$.

As a result, the regression explains 36.7 percent of the variation in the observed values of the response variable. It can be interpreted as the linear relationship between the inauguration $\left(x\right)$and death $\left(y\right)$ accounts for $36.7$ percent of the variability in death.

Part d Step 1 Given Information

The information Please A/mana provides data on the ages at the inauguration and of death for the presidents of the United States. We give those data on the WeissStats site for those presidents who are not still living at the time of this writing. 

Part d Step 2 Explanation

The determination coefficient will be$0.367$.

As a result, the regression explains 36.7 percent of the variation in the observed values of the response variable. It can be interpreted as the linear relationship between the inauguration$\left(x\right)$ and death $\left(y\right)$accounts for $36.7$ percent of the variability in death.

The regression equation cannot be used to make predictions because the percentage of variation in the observed values of the response variable explained by the regression is less than $50$ percent.