Chapter PII, Problem 34RE

(a)

To determine

To create a linear model to predict the number of gallons that will be available in $2005$ .

Answer to Problem 34RE

The regression line is .

Explanation of Solution

It is given in the question that since clean air regulations have dictated the use of unleaded gasoline the supply of leaded gas in New York State has diminished. The table is given on the August New York State Math B exam, a state wide achievement test for high school students. Thus, for constructing a linear model we will use Excel as we will first select the data in Excel and then go to the insert tab from where we will select the scatterplot option in the charts and when the scatterplot is constructed we will go to the design tab under the chart tools, from where we will select the quick layout option and select the layout with the equation option then the linear model is constructed in the scatterplot as:

  

Thus, the regression line is as:

  

(b)

To determine

To explain why that method is incorrect.

Explanation of Solution

It is given in the question that since clean air regulations have dictated the use of unleaded gasoline the supply of leaded gas in New York State has diminished. The table is given on the August New York State Math B exam, a state wide achievement test for high school students. And the regression line is:

  

Since the exam asked the students to estimate the year when leaked gasoline will first become unavailable, expecting them to use the model from part (a) to answer the question so, we cannot use that model in part (a) because the model predicts gallons from year not the other way around.

(c)

To determine

To create a model that would be appropriate for that task and make the estimate.

Answer to Problem 34RE

The model is .

Explanation of Solution

It is given in the question that since clean air regulations have dictated the use of unleaded gasoline the supply of leaded gas in New York State has diminished. The table is given on the August New York State Math B exam, a state wide achievement test for high school students. And the regression line is:

  

Thus, the model to predict the year from the gallons can be created by using Excel as we will first select the data in Excel and then go to the insert tab from where we will select the scatterplot option in the charts and when the scatterplot is constructed we will go to the design tab under the chart tools, from where we will select the quick layout option and select the layout with the equation option then the linear model is constructed in the scatterplot as:

  

Thus, the linear model is as:

  

(d)

To determine

To explain why the wrong answer from the other model is fairly accurate in this case.

Explanation of Solution

It is given in the question that since clean air regulations have dictated the use of unleaded gasoline the supply of leaded gas in New York State has diminished. The table is given on the August New York State Math B exam, a state wide achievement test for high school students. Thus, the wrong answer from the other model is fairly accurate in this case because if we solve for the value it will be close but the model cannot predict changes.