The computer output (below) shows a relationship where Y = Sale price for a home, X₁ = living area, and X₂ = # of bedrooms, X₃ = # of bathrooms. We would like to predict Price (Y). There are three 2-variable regression relationships shown and one 4-variable multiple regression relationship shown.

Regression Equation

Price

=

171032 +120420Bathrooms

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
267458	14.27%	14.17%	13.82%

Regression Equation

Price

=

200274 +113.68LivingArea

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
268449	13.54%	13.44%	13.10%

Regression Equation

Price

=

338975 +40234Bedrooms

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
286741	1.35%	1.24%	0.92%

**Multiple regression output is below:

Regression Equation

Price

=

275641 +84.7LivingArea -66797Bedrooms +93925Bathrooms

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
260320	18.97%	18.69%	18.21%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	275641	40655	6.78	0.000

Final multiple regression relationship:

Coefficients

Term Coef SE Coef T-Value P-Value

Constant 275641 40655 6.78 0.000

Living Area 84.7 13.4 6.33 0.000

Bedrooms -66797 13089 -5.10 0.000

Bathrooms 93925 13660 6.88 0.000

Model Summary

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

260320 18.97% 18.69% 18.21%

What is the independent variable that has the most influence in predicting Price? Explain your reasoning.