Chapter 12.2, Problem 36E

(a)

To determine

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

Answer to Problem 36E

  $\frac{1}{\widehat{y}}=0.100170+0.0398119x$

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

  $b_0$ =0.100170

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

  $b_1$ =0.0398119

Putting the value of $b_0$ and $b_1$

  $\begin{array}{l}\widehat{y}=b_0+b_{1}x\\ \widehat{y}=0.100170+0.0398119x\end{array}$

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

  $\frac{1}{\widehat{y}}=0.100170+0.0398119x$

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 36E

1.2870 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 $x$

  $\begin{array}{l}\frac{1}{\widehat{y}}=0.100170+0.0398119x\\ \frac{1}{\widehat{y}}=0.100170+0.0398119\left(17\right)=0.7769723\\ \widehat{y}=\frac{1}{0.7769723}=1.2870\end{array}$

Therefore the expected volume is 1.2870 atm.