Stats: Modeling the World Nasta Edition Grades 9-12
Stats: Modeling the World Nasta Edition Grades 9-12
3rd Edition
ISBN: 9780131359581
Author: David E. Bock, Paul F. Velleman, Richard D. De Veaux
Publisher: PEARSON
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Chapter 8, Problem 31E

(a)

To determine

To write the equation of the regression line.

(a)

Expert Solution
Check Mark

Answer to Problem 31E

  N^ icotine=0.15403+0.065052Tar .

Explanation of Solution

In the previous question, it is given the researcher wants to find out is the nicotine content of a cigarette related to the “tars”. Thus, a collection of data in milligrams on 29 cigarettes produced the scatterplot, residual plot and the regression analysis shown in the question. And also it is given that,

  R2=92.4%

  Constant=0.154030Tar=0.065052

And the dependent variable is nicotine. Thus, the regression line will be:

  N^ icotine=0.15403+0.065052Tar

(b)

To determine

To estimate the nicotine content of cigarettes with 4 milligrams of tar.

(b)

Expert Solution
Check Mark

Answer to Problem 31E

  0.414 milligrams.

Explanation of Solution

In the previous question, it is given the researcher wants to find out is the nicotine content of a cigarette related to the “tars”. Thus, a collection of data in milligrams on 29 cigarettes produced the scatterplot, residual plot and the regression analysis shown in the question. And also it is given that,

  R2=92.4%

  Constant=0.154030Tar=0.065052

And the dependent variable is nicotine. And, the regression line is:

  N^ icotine=0.15403+0.065052Tar

Thus, the nicotine content of cigarettes with 4 milligrams of tar is calculated as:

  N^ icotine=0.15403+0.065052Tar=0.15403+0.065052×4=0.414

The nicotine will be 0.414 milligrams.

(c)

To determine

To interpret the meaning of the slope of the regression line in this context.

(c)

Expert Solution
Check Mark

Explanation of Solution

In the previous question, it is given the researcher wants to find out is the nicotine content of a cigarette related to the “tars”. Thus, a collection of data in milligrams on 29 cigarettes produced the scatterplot, residual plot and the regression analysis shown in the question. And also it is given that,

  R2=92.4%

  Constant=0.154030Tar=0.065052

And the dependent variable is nicotine. And, the regression line is:

  N^ icotine=0.15403+0.065052Tar

Thus, the meaning of the slope of the regression line in this context is that predicted nicotine content increases by 0.065 milligram of nicotine per additional milligram of tar.

(d)

To determine

To explain what does the y -intercept mean.

(d)

Expert Solution
Check Mark

Answer to Problem 31E

Explanation of Solution

In the previous question, it is given the researcher wants to find out is the nicotine content of a cigarette related to the “tars”. Thus, a collection of data in milligrams on 29 cigarettes produced the scatterplot, residual plot and the regression analysis shown in the question. And also it is given that,

  R2=92.4%

  Constant=0.154030Tar=0.065052

And the dependent variable is nicotine. And, the regression line is:

  N^ icotine=0.15403+0.065052Tar

Thus the y -intercept means that we had expect a cigarette with no tar to have 0.154 milligrams of nicotine.

(e)

To determine

To find out what is the nicotine content.

(e)

Expert Solution
Check Mark

Answer to Problem 31E

  0.1094 mg of nicotine.

Explanation of Solution

In the previous question, it is given the researcher wants to find out is the nicotine content of a cigarette related to the “tars”. Thus, a collection of data in milligrams on 29 cigarettes produced the scatterplot, residual plot and the regression analysis shown in the question. And also it is given that,

  R2=92.4%

  Constant=0.154030Tar=0.065052

And the dependent variable is nicotine. And, the regression line is:

  N^ icotine=0.15403+0.065052Tar

It is given if a new brand of cigarette contains 7 milligrams of tar and a nicotine level whose residual is 0.5 mg then the nicotine content will be as:

  N^ icotine=0.15403+0.065052Tar=0.15403+0.065052×7=0.609Residual=Actualpredicted0.5=Actual0.609Actual=0.6090.5=0.1094

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