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Chapter 4: Q. 4.106 (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 4.74 on domestic and overseas grosses for a random sample of 50movies are on the WeissStats site.

Short Answer

Expert verified

(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 0.7264.

(c) The percentage of variation in the observed values of the response variable explained by the regression is 72.64%.

(d)The regression equation is useful for making predictions because the percentage of variation in the observed values of the response variable explained by the regression is 72.64%which is greater than 50%.

Step by step solution

01

Part (a) Step 1. Given Information. 

The data from Exercise 4.74 on domestic and overseas grosses for a random sample of 50movies are on the WeissStats site.

02

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 Overseas and under X-variables enter a column of Domestic.

4. Click OK.

03

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.

04

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 Overseas.

3. In predictors, enter the column Birdies.Domestic.

4. Click OK.

05

Part (b) Step 2. The MINITAB output 

The MINITAB output is:

From the MINITAB output, the coefficient of determination is0.7264.

06

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 is72.64%.

07

Part (d) Step 1. Explanation. 

The regression equation is useful for making predictions because the percentage of variation in the observed values of the response variable explained by the regression is 72.64%which is greater than50%.

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