The Practice of Statistics for AP - 4th Edition
The Practice of Statistics for AP - 4th Edition
4th Edition
ISBN: 9781429245593
Author: Starnes, Daren S., Yates, Daniel S., Moore, David S.
Publisher: Macmillan Higher Education
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Chapter 12.2, Problem 36E

(a)

To determine

To give the equation of the least squares regression line.

(a)

Expert Solution
Check Mark

Answer to Problem 36E

Transformation 1 : P^ ressure=0.36774+15.8994×1Volume

Transformation 2 : 1 P^ ressure=0.15465+0.042836×Volume

Explanation of Solution

In the question there are two transformations given and the computer output for each is also given. Thus, we have,

For transformation 1 :

Thus, the general equation of the regression equation is as:

   P^ ressure=a+b×1Volume

Thus, the value of the slope and the constant is given in the computer output as:

  a=0.36774b=15.8994

Thus, the regression equation is as follows:

   P^ ressure=a+b×1Volume P^ ressure=0.36774+15.8994×1Volume

For transformation 2 :

Thus, the general equation of the regression equation is as:

  1 P^ ressure=a+b×Volume

Thus, the value of the slope and the constant is given in the computer output as:

  a=0.100170b=0.0398119

Thus, the regression equation is as follows:

  1 P^ ressure=a+b×Volume1 P^ ressure=0.15465+0.042836×Volume

(b)

To determine

To use the model from part (a) to predict the pressure in the syringe when the volume is 17 cubic centimeter.

(b)

Expert Solution
Check Mark

Answer to Problem 36E

Transformation

  1 : 1.303

Transformation 2 : 1.287

Explanation of Solution

Thus, we need to find out the period of a pendulum with the length 80 centimeters using the part (a) as:

For transformation 1 :

Thus, the regression equation is as follows:

   P^ ressure=a+b×1Volume P^ ressure=0.36774+15.8994×1Volume

Then by evaluating we have,

   P^ ressure=a+b×1Volume P^ ressure=0.36774+15.8994×1Volume=0.36774+15.8994×117=1.303

For transformation 2 :

Thus, the regression equation is as follows:

  1 P^ ressure=a+b×Volume1 P^ ressure=0.15465+0.042836×Volume

Then by evaluating we have,

  1 P^ ressure=a+b×Volume1 P^ ressure=0.15465+0.042836×Volume1 P^ ressure=0.15465+0.042836×171 P^ ressure=0.7769723 P^ ressure=10.7769723 P^ ressure=1.287

(c)

To determine

To interpret the value of s in this context.

(c)

Expert Solution
Check Mark

Explanation of Solution

As we need to interpret the value of s in this context. Thus, we have,

For transformation 1 :

Thus, the regression equation is as follows:

   P^ ressure=a+b×1Volume P^ ressure=0.36774+15.8994×1Volume

And the value of s is given as,

  s=0.044205

This means that the expected error from the prediction of the pressure is 0.044205 .

For transformation 2 :

Thus, the regression equation is as follows:

  1 P^ ressure=a+b×Volume1 P^ ressure=0.15465+0.042836×Volume

And the value of s is given as,

  s=0.00398119

This means that the expected error from the prediction of the reciprocal of the pressure is 0.00398119 .

Chapter 12 Solutions

The Practice of Statistics for AP - 4th Edition

Ch. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.1 - Prob. 10ECh. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Prob. 32ECh. 12.2 - Prob. 1.1CYUCh. 12.2 - Prob. 1.2CYUCh. 12.2 - Prob. 1.3CYUCh. 12.2 - Prob. 1.4CYUCh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.2 - Prob. 50ECh. 12.2 - Prob. 51ECh. 12.2 - Prob. 52ECh. 12 - Prob. 1CRECh. 12 - Prob. 2CRECh. 12 - Prob. 3CRECh. 12 - Prob. 4CRECh. 12 - Prob. 5CRECh. 12 - Prob. 6CRECh. 12 - Prob. 1PTCh. 12 - Prob. 2PTCh. 12 - Prob. 3PTCh. 12 - Prob. 4PTCh. 12 - Prob. 5PTCh. 12 - Prob. 6PTCh. 12 - Prob. 7PTCh. 12 - Prob. 8PTCh. 12 - Prob. 9PTCh. 12 - Prob. 10PTCh. 12 - Prob. 11PTCh. 12 - Prob. 12PTCh. 12 - Prob. 1PT4Ch. 12 - Prob. 2PT4Ch. 12 - Prob. 3PT4Ch. 12 - Prob. 4PT4Ch. 12 - Prob. 5PT4Ch. 12 - Prob. 6PT4Ch. 12 - Prob. 7PT4Ch. 12 - Prob. 8PT4Ch. 12 - Prob. 9PT4Ch. 12 - Prob. 10PT4Ch. 12 - Prob. 11PT4Ch. 12 - Prob. 12PT4Ch. 12 - Prob. 13PT4Ch. 12 - Prob. 14PT4Ch. 12 - Prob. 15PT4Ch. 12 - Prob. 16PT4Ch. 12 - Prob. 17PT4Ch. 12 - Prob. 18PT4Ch. 12 - Prob. 19PT4Ch. 12 - Prob. 20PT4Ch. 12 - Prob. 21PT4Ch. 12 - Prob. 22PT4Ch. 12 - Prob. 23PT4Ch. 12 - Prob. 24PT4Ch. 12 - Prob. 25PT4Ch. 12 - Prob. 26PT4Ch. 12 - Prob. 27PT4Ch. 12 - Prob. 28PT4Ch. 12 - Prob. 29PT4Ch. 12 - Prob. 30PT4Ch. 12 - Prob. 31PT4Ch. 12 - Prob. 32PT4Ch. 12 - Prob. 33PT4Ch. 12 - Prob. 34PT4Ch. 12 - Prob. 35PT4Ch. 12 - Prob. 36PT4Ch. 12 - Prob. 37PT4Ch. 12 - Prob. 38PT4Ch. 12 - Prob. 39PT4Ch. 12 - Prob. 40PT4Ch. 12 - Prob. 41PT4Ch. 12 - Prob. 42PT4Ch. 12 - Prob. 43PT4Ch. 12 - Prob. 44PT4Ch. 12 - Prob. 45PT4Ch. 12 - Prob. 46PT4
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