Shown below is output from two Excel regression analyses on the same problem. The first output was done on a “full” model. In the second output, the variable with the smallest absolute t value has been removed, and the regression has been rerun like a second step of a backward elimination process. Examine the two outputs. Explain what happened, what the results mean, and what might happen in a third step. FULL MODEL Regression Statistics Multiple R 0.567 R Square 0.321 Adjusted R Square 0.208 Standard Error 159.681 Observations 29 ANOVA Significance df SS MS F F Regression 4 289856.08 72464.02 2.84 0.046 Residual 24 611955.23 25498.13 Total 28 901811.31 Coefficients Standard Error t Stat P-value Intercept 336.79 124.0800 2.71 0.012 X1 1.65 1.7800 0.93 0.363 X2 −5.63 13.4700 −0.42 0.680 X3 0.26 1.6800 0.16 0.878 X4 185.50 66.2200 2.80 0.010 SECOND MODEL Regression Statistics Multiple R 0.566 R Square 0.321 Adjusted R Square 0.239 Standard Error 156.534 Observations 29 ANOVA Significance df SS MS F F Regression 3 289238.1 96412.70 3.93 0.020 Residual 25 612573.20 24502.90 Total 28 901811.3 Coefficients Standard Error t Stat P-value Intercept 342.92 11.34 2.97 0.006 X1 1.83 1.31 1.40 0.174 X2 −5.75 13.18 −0.44 0.667 X4 181.22 59.05 3.07 0.005

Shown below is output from two Excel regression analyses on the same problem. The first output was done on a “full” model. In the second output, the variable with the smallest absolute t value has...

Shown below is output from two Excel regression analyses on the same problem. The first output was done on a “full” model. In the second output, the variable with the smallest absolute t value has been removed, and the regression has been rerun like a second step of a backward elimination process. Examine the two outputs. Explain what happened, what the results mean, and what might happen in a third step.

FULL MODEL
Regression Statistics
Multiple R	0.567
R Square	0.321
Adjusted R Square	0.208
Standard Error	159.681
Observations	29

ANOVA
				Significance
	df	SS	MS	F	F
Regression	4	289856.08	72464.02	2.84	0.046
Residual	24	611955.23	25498.13
Total	28	901811.31

	Coefficients	Standard Error	t Stat	P-value
Intercept	336.79	124.0800	2.71	0.012
X₁	1.65	1.7800	0.93	0.363
X₂	−5.63	13.4700	−0.42	0.680
X₃	0.26	1.6800	0.16	0.878
X₄	185.50	66.2200	2.80	0.010

SECOND MODEL
Regression Statistics
Multiple R	0.566
R Square	0.321
Adjusted R Square	0.239
Standard Error	156.534
Observations	29

ANOVA
				Significance
	df	SS	MS	F	F
Regression	3	289238.1	96412.70	3.93	0.020
Residual	25	612573.20	24502.90
Total	28	901811.3

	Coefficients	Standard Error	t Stat	P-value
Intercept	342.92	11.34	2.97	0.006
X₁	1.83	1.31	1.40	0.174
X₂	−5.75	13.18	−0.44	0.667
X₄	181.22	59.05	3.07	0.005

May 25, 2022

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Shown below is output from two Excel regression analyses on the same problem. The first output was done on a “full” model. In the second output, the variable with the smallest absolute t value has...

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