Question

In: Statistics and Probability

Determine the regression equatoin for this multiple regression model. Also calculate the adjusted R squared and...

Determine the regression equatoin for this multiple regression model. Also calculate the adjusted R squared and P value.

Pedictor Variables/Data
Length (inches)	Braking (ft from 60 mph)	Engine Displacement (liters)	GHG
154	133	1.6	6.6
167	132	1.6	6.1
177	136	1.8	6.3
177	138	2	6.6
179	137	2	6.4
188	135	2	8.0
177	126	2	7.7
191	136	2.3	8.0
194	140	2.4	7.7
189	137	2.4	7.3
180	135	2.5	8.3
190	136	2.5	7.1
180	140	2.5	8.0
200	131	2.7	8.7
193	134	3.3	8.7
191	128	3.5	8.3
197	139	3.5	8.0
208	145	4.6	10.2
203	143	4.6	10.2
212	140	4.6	9.6
215	143	4.6	9.6

Expert Solution

Using Excel we get following output

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.911590634
R Square	0.830997484
Adjusted R Square	0.801173511
Standard Error	0.54976783
Observations	21

ANOVA
	df		SS		MS		F		Significance F
Regression	3		25.2647		8.421566		27.86341		8.65122E-07
Residual	17		5.138159		0.302245
Total	20		30.40286
		Coefficients		Standard Error		t Stat		*P-value*
Intercept		5.359938521		4.559404882		1.175579		0.255965
Length (inches)		0.018520385		0.016658021		1.1118		0.281701
Braking (ft from 60 mph)		-0.02522475		0.031380555		-0.80383		0.43259
Engine Displacement (liters)		0.910291795		0.244316648		3.725869		0.001681

Using minitab we get following output:

Regression Analysis: GHG versus Length (inches), Braking (ft from, Engine Displacem

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value

Regression 3 25.2647 8.4216 27.86 0.000

Length (inches) 1 0.3736 0.3736 1.24 0.282

Braking (ft from 60 mph) 1 0.1953 0.1953 0.65 0.433

Engine Displacement (liters) 1 4.1958 4.1958 13.88 0.002

Error 17 5.1382 0.3022

Total 20 30.4029

Model Summary

S R-sq R-sq(adj) R-sq(pred)

0.549768 83.10% 80.12% 74.04%

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant 5.36 4.56 1.18 0.256

Length (inches) 0.0185 0.0167 1.11 0.282 4.04

Braking (ft from 60 mph) -0.0252 0.0314 -0.80 0.433 1.50

Engine Displacement (liters) 0.910 0.244 3.73 0.002 4.24

Regression Equation

GHG = 5.36 + 0.0185 Length (inches) - 0.0252 Braking (ft from 60 mph)

+ 0.910 Engine Displacement (liters)

Using above result from minitab and excel we get

Multiple regression model is given by,

GHG = 5.36 + 0.0185 Length (inches) - 0.0252 Braking (ft from 60 mph)

+ 0.910 Engine Displacement (liters) (Rounded value)

OR

GHG = 5.35994 + 0.018520385 Length (inches)-0.02522475 Braking (ft from 60 mph)

+ 0.910291795 Engine Displacement (liters)

Adujested R_Sq is

R-sq(adj)= 80.12%

P value is given by

	P-value	Rounded P-value
Intercept	0.255965414	0.256
Length (inches)	0.281700818	0.282
Braking (ft from 60 mph)	0.432590092	0.433
Engine Displacement (liters)	0.001680723	0.002

Steps involve in minitab

Copy data > Stat >Regression > Regression > Fit Regression model > Select Response variable (GHG), Select predictor variable one by one (Length,Braking,Engine Displacement)>ok.

IN Excel

Copy data > Data> Data Analysis > Regression > select Response Range (GHG), select all predictor (Length,Braking,Engine Displacement) >ok

orchestra answered 3 years ago

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