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Mobile App Chapter 4: Q. 4.105 (page 182)
In Exercises 4.104 - 4.115, use the technology of your choice to perform the following tasks.
(a) Decide whether finding the regression line for the data is reasonable. If so, do parts (b) - (d).
(b) Obtain the coefficient of determination,
(c) Determine the percentage of variation in the observed values of the response variable explained by the regression and interpret your answer.
(d) State how useful the regression equation appears to be for making predictions.
The data from Exercise 4.71 for the ages at inauguration and for the death of the Presidents of the United States are on the WeissStats site.
Short Answer
(a) From the scatterplot, it is reasonable to find the regression line for the data since the observations are around the line.
(b) The coefficient of determination is 0.367.
(c) The percentage of variation in the observed values of the response variable explained by the regression is 36.7%.
(d)The regression equation is not useful for making predictions because the percentage of variation in the observed values of the response variable explained by the regression is 36.7%which is less than 50%.
Step by step solution
Part (a) Step 1. Given Information.
The data from Exercise 4.71 for the ages at inauguration and for the death of the Presidents of the United States are on the WeissStats site.
Part (a) Step 2. The MINITAB procedure.
The MINITAB procedure for constructing scatterplot is:
1. Choose Graph > Scatterplot.
2. Choose with Connect Line, click OK.
3. Under Y-variables, enter a column of Death and under X-variables enter a column of Inauguration.
4. Click OK.
Part (a) Step 3. Graph the scatterplot.
The MINITAB output is:
From the scatterplot, it is reasonable to find the regression line for the data since the observations are around the line.
Part (b) Step 1. The MINITAB procedure.
The MINITAB procedure for finding the coefficient of determination is:
1. Choose Stat > Regression > Regression.
2. In response, enter the column Death.
3. In predictors, enter the column Inauguration.
4. Click OK.
Part (b) Step 2. The MINITAB output
The MINITAB output is:
From the MINITAB output, the coefficient of determination is0.367.
Part (c) Step 1. Find the percentage of variation.
From the MINITAB output, the percentage of variation in the observed values of the response variable explained by the regression is36.7%.
Part (d) Step 1. Explanation.
The regression equation is not useful for making predictions because the percentage of variation in the observed values of the response variable explained by the regression is 36.7%which is less than50%.
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