Following data are recorded to investigate the relationship between 3 inputs X ₁ , X ₂ and X ₃ and the output Y

X1	X2	X3	Y
3	2	1	4.635801337
3	2	1.5	8.43023389
4	6	2	7.537262868
2	2	3	20.74872142
1	2	4	16.7683904
5	1.5	2	37.59973946
3	1.5	2.5	31.74031713
4	3	1	3.899022628
1.5	2	2	7.359166777
3	2	2.5	23.70273779
1	3	1	1.050679772
2	2	4	37.30251696

a) Using the data analysis package in excel to find the regression relationship among X ₁ , X ₂ , X ₃ , and Y

b) Once finishing analysis data in step a, one inspector suspected that the relationship among these factors is not linear. As a result of that, the inspector decided to transform the data. The inspector suspect that the relationship of these factors is under the form

y= β ₀ X ₁ ^{β 1} X ₂ ^{β ₂} X ₃ ^{β ₃}

To make data transform, firstly, 2 sides of the equation are transformed into natural logarithm then the regression is conducted.

Using the data analysis package in excel to find the regression relationship.