The density of an oil mixture (mix) as a function of the temperature (T) and the...

The density of an oil mixture (mix) as a function of the temperature (T) and the mass fraction of the three components (mi) was measured and results are shown :

T (K) m1 m2 m3 Pmix (kg/m3 )

300 0 1 0 879.6

320 0 0.5 0.5 870.6

340 0 0 1 863.6

360 0.5 0 0.5 846.4

380 0.5 0.25 0.25 830.8

400 0.5 0.5 0 819.1

420 1 0 0 796

440 1 0 0 778.2

Find the coefficients for a multiple regression of the form Pmix = a0 + a1*T + a2*m1 + a3*m2 + a4*m3

Solutions

Expert Solution

The regression output is:

Regression Statistics
Multiple R	0.995394
R Square	0.990809
Adjusted R Square	0.733916
Standard Error	4.602693
Observations	8

ANOVA
	df	SS	MS	F	Significance F
Regression	4	9135.08	2283.77	143.7365	0.000932
Residual	4	84.73914	21.18478
Total	8	9219.819

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1044.391	48.54099	21.51566	2.76E-05	909.6199	1179.163	909.6199	1179.163
T	-0.59204	0.112089	-5.2819	0.006162	-0.90325	-0.28083	-0.90325	-0.28083
m1	0	0	65535	#NUM!	0	0	0	0
m2	14.34136	14.2508	1.006355	#NUM!	-25.2252	53.90792	-25.2252	53.90792
m3	21.93406	12.5917	1.741947	0.156482	-13.0261	56.89422	-13.0261	56.89422

Pmix = 1044.391 -0.59204*T + 0*m1 + 14.34136*m2 + 21.93406*m3

milcah answered 1 week ago

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