Question

In: Statistics and Probability

End of Section Problem 13.12 Your answer is partially correct. Try again. Use the following data...

End of Section Problem 13.12


	Your answer is partially correct. Try again.

Use the following data to develop a regression model to predict y from x1 and x2. Comment on the output.
Develop a regression model to predict y from x1 only. Compare the results of this model with those of the model using both predictors.What might you conclude by examining the output from both regression models?

y	x₁	x₂
28	12.6	134
43	11.4	126
45	11.5	143
49	11.1	152
57	10.4	143
68	9.6	147
74	9.8	128
81	8.4	119
82	8.8	130
86	8.9	135
101	8.1	141
112	7.6	123
114	7.8	121
119	7.4	129
124	6.4	135

(Round all answers to 4 decimal places.)

The regression equation for y from x1 and x2 is:

) x1 +(

) x2

with p=

tx1=

with p=

tx2=

with p=

The regression equation for y from x1 only is:

) x1

with p=

Solutions

Expert Solution

Using Excel, go to Data select Data Analysis, choose Regression. Put y values in Y input range. Put x1 and x2 values in X input range for first model and put x1 values in X input range for second model.

x1 and x2 model

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.9814
R Square	0.9632
Adjusted R Square	0.9570
Standard Error	6.3334
Observations	15

ANOVA
	df	SS	MS	F	Significance F
Regression	2	12586.3823	6293.1912	156.8882	0.0000
Residual	12	481.3510	40.1126
Total	14	13067.7333

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	243.4408	23.0195	10.5754	0.0000	193.2856	293.5961
X1	-16.6079	1.0312	-16.1047	0.0000	-18.8548	-14.3610
X2	-0.0732	0.1870	-0.3915	0.7023	-0.4806	0.3342

The regression equation for y from x1 and x2 is:

y = 243.4408 + (-16.6079)x1 +(-0.0732)x2

F = 156.8882

with p = 0.000

tx1 = -16.1047

with p = 0.000

tx2 = -0.3915

with p = 0.7023

x1 model

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.9812
R Square	0.9627
Adjusted R Square	0.9598
Standard Error	6.1237
Observations	15

ANOVA
	df	SS	MS	F	Significance F
Regression	1	12580.2357	12580.2357	335.4746	0.0000
Residual	13	487.4976	37.4998
Total	14	13067.7333

	Coefficients	Standard Error	t Stat	P-value
Intercept	235.1429	8.6775	27.0980	0.0000
X1	-16.7678	0.9155	-18.3160	0.0000

The regression equation for y from x1 and x2 is:

y = 235.1429 + (-16.7678)x1

F = 335.4746

with p = 0.000

orchestra answered 1 year ago

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