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Boyle鈥檚 law Refer to Exercise 34. Here is a graph of 1Pressureversus 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 17cubic centimeters.

Short Answer

Expert verified

a). The equation of the least-squares regression line is 1y^=0.100170+0.0398119x.

b). The expected volume is 1.2870atm.

Step by step solution

01

Part (a) Step 1: Given Information

Given data:

02

Part (a) Step 2: Explanation

Least square regression line's general equation

y^=b0+b1x

The computed value of the constant b0appears in the row "constant" and the column "Coef" of the computer output.

b0=0.100170

In the row "volume" and the column "Coef" of the computer's output, the calculated slope b1is mentioned.

b1=0.0398119
03

Part (a) Step 3: Explanation

Substituting the value of b0 and b1:

y^=b0+b1x

y^=0.100170+0.0398119x

Where xdenotes volume and yis the reciprocal of pressure.

localid="1654258726837" 1y^=0.100170+0.0398119x

xdenotes volume, while ydenotes pressure.

04

Part (b) Step 1: Given Information

Given data:

05

Part (b) Step 2: Explanation

The least-squares regression line's equation is:

y^=0.36774+15.89941x

xdenotes volume, while ydenotes pressure.

Substituting the value of x:

1y^=0.100170+0.0398119x

1y^=0.100170+0.0398119(17)

=0.7769723

=10.7769723

=1.2870

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