Question

Boyle’s law Refer to Exercise 34. Here is a graph of $\frac{1}{Pressure}$versus volume along with output from a linear regression analysis using these variables:

a. Give the equation of the least-squares regression line. Define any variables you use. b. Use the model from part (a) to predict the pressure in the syringe when the volume is $17$cubic centimeters.

Short answer

a). The equation of the least-squares regression line is $\frac{1}{\hat{y}}=0.100170+0.0398119x$.

b). The expected volume is $1.2870\mathrm{atm}$.

Step-by-step solution

Part (a) Step 1: Given Information

Given data:

Part (a) Step 2: Explanation

Least square regression line's general equation

$\hat{y}=b_0+b_{1}x$

The computed value of the constant $b_0$appears in the row "constant" and the column "Coef" of the computer output.

$b_0=0.100170$

In the row "volume" and the column "Coef" of the computer's output, the calculated slope $b_1$is mentioned.

$b_1=0.0398119$

Part (a) Step 3: Explanation

Substituting the value of $b_0$ and $b_1$:

$\hat{y}=b_0+b_{1}x$

$\hat{y}=0.100170+0.0398119x$

Where $x$denotes volume and $y$is the reciprocal of pressure.

localid="1654258726837" $\frac{1}{\hat{y}}=0.100170+0.0398119x$

$x$denotes volume, while $y$denotes pressure.

Part (b) Step 1: Given Information

Given data:

Part (b) Step 2: Explanation

The least-squares regression line's equation is:

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

$x$denotes volume, while $y$denotes pressure.

Substituting the value of $x$:

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

$\frac{1}{\hat{y}}=0.100170+0.0398119\left(17\right)$

$=0.7769723$

$=\frac{1}{0.7769723}$

$=1.2870$