Chapter PII, Problem 36RE

(a)

To determine

To fit a straight line to the relationship between weight and year.

Answer to Problem 36RE

The line is .

Explanation of Solution

It is given in the question that the sears cup was established to honour institutions that maintain a broad based athletics program achieving success in many sports both men’s and women’s. And the table is also given which shows the average team weights for selected years. Thus, for fitting a straight line to the relationship between weight and year 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 equation for the regression line will be as:

  

(b)

To determine

To explain does a straight line seems reasonable.

Answer to Problem 36RE

No, straight line does not seems to be reasonable.

Explanation of Solution

It is given in the question that the sears cup was established to honour institutions that maintain a broad based athletics program achieving success in many sports both men’s and women’s. And the table is also given which shows the average team weights for selected years. Thus, the straight line does not seemto be reasonable because weight cannot increase indefinitely and that leads to extrapolation.

(c)

To determine

To predict the average weight of the team for the year $2003$ and explain does this seems reasonable.

Answer to Problem 36RE

The average weight of the team for the year $2003$ is $214.77$ pounds and it seems reasonable.

Explanation of Solution

It is given in the question that the sears cup was established to honour institutions that maintain a broad based athletics program achieving success in many sports both men’s and women’s. And the regression line is . Thus, the average weight of the team for the year $2003$ is predicted as:

  

The predicted weight is $214.77$ pounds and this seems to be reasonable because the weight falls close to the weights already plotted out $214.77$ pounds.

(d)

To determine

To explain what about the prediction for the year $2103$ .

Answer to Problem 36RE

The average weight is $323.91$ pounds and it does not seem reasonable.

Explanation of Solution

It is given in the question that the sears cup was established to honour institutions that maintain a broad based athletics program achieving success in many sports both men’s and women’s. And the regression line is . Thus, the average weight of the team for the year $2103$ is predicted as:

  

The average weight is $323.91$ pounds and this does not seems to be reasonable because $323.91$ pounds is larger than the weights used to find by the model by a factor of $1.5$ and is using a lot of extrapolation.

(e)

To determine

To explain what about the prediction for the year $3003$ .

Answer to Problem 36RE

The average weight is $1306.17$ pounds and it does not seem reasonable.

Explanation of Solution

It is given in the question that the sears cup was established to honour institutions that maintain a broad based athletics program achieving success in many sports both men’s and women’s. And the regression line is . Thus, the average weight of the team for the year $3003$ is predicted as:

  

The average weight is $1306.17$ pounds and this does not seems to be reasonable because $1306.17$ pounds is larger than the weights used to find by the model and is using a lot of extrapolation.