Chapter 12.2, Problem 34E

(a)

To determine

To find: the equation of the least-squares regression line.

Answer to Problem 34E

  $\widehat{y}=0.36774+15.8994\times \frac{1}{x}$

Explanation of Solution

Given:

  

  

Calculation:

General equation for the least square regression line

  $\widehat{y}=b_0+b_{1}x$

The calculated of the constant $b_0$ is mention in the row “constant” and in the column “Coef” of the output of the computer

  $b_0$ =0.36774

The calculated of the slope $b_1$ is mention in the row “1/V and in the column “Coef” of the output of the computer

  $b_1$ =15.8994

Putting the value of $b_0$ and $b_1$

  $\begin{array}{l}\widehat{y}=b_0+b_{1}x\\ \widehat{y}=0.36774+15.8994x\end{array}$

Where x shows the reciprocal of the volume and y shows the pressure

  $\widehat{y}=0.36774+15.8994\times \frac{1}{x}$

Where $x$ is representing the volume and y is representing the pressure

(b)

To determine

To Explain: the prediction of the pressure in the syringe if the volume is 17 cubic cm using the part (a)

Answer to Problem 34E

1.3030 atm

Explanation of Solution

Given:

  

  

Calculation:

From the part (a)

  $\widehat{y}=0.36774+15.8994\times \frac{1}{x}$

Where $x$ is representing the volume and y is representing the pressure

Putting the value of $x$

  $\begin{array}{l}\widehat{y}=0.36774+15.8994\times \frac{1}{17}\\ \widehat{y}=1.3030\end{array}$

Therefore the expected pressure is 1.3030 atm.