Chapter 10, Problem 14E

To determine

To construct: the appropriate model on the basis of given data.

Explanation of Solution

Given:

Height	Pressure
48	29.1
44	31.9
40	35.3
36	39.3
32	44.2
28	50.3
24	58.8
20	70.7
18	77.9
16	87.9
14	100.4
12	117.6

Graph:

  

This scatter figure of data is to know about the relationship between the variables. It represents the association between the height of the cylinder and pressure inside the cylinder. Therefore, linear model would not be fit into the data well.

Height	1/Pressure
48	0.034364261
44	0.031347962
40	0.028328612
36	0.025445293
32	0.022624434
28	0.019880716
24	0.017006803
20	0.014144272
18	0.01283697
16	0.011376564
14	0.009960159
12	0.008503401

Again plotting the graph

  

Regression output of the estimated table

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-7.6697E-05	7.81321E-05	-0.981632891	0.349433095	-0.000250786	9.73921E-05	-0.000250786	9.73921E-05
X Variable 1	0.000713072	2.59959E-06	274.3012033	1.0199E-20	0.000707279	0.000718864	0.000707279	0.000718864

Therefore the required equation from the above of the regression equation

  $\frac{1}{\text{Pressure}}=-0.000077+0.000713\times Height$

R-squared of the model is, about 100 percent which implies 100 percent of variability in the reciprocal of pressure is estimated for by the model.