The estimated regression equation for a model involving two independent variable

Question

The estimated regression equation for a model involving two independent variables and 10 observations follows.

= 33.1848 + 0.5817x1 + 0.5412x2

Interpret b1 and b2 in this estimated regression equation.

b1
Select one:

y changes by 0.5817 when x1 increases by 1 unit and x2 stays the same

y changes by 0.5817 when x2 increases by 1 unit and x1 stays the same

x1 changes by 0.5817 when x2 increases by 1 unit and y stays the same

x2 changes by 0.5817 when x1 increases by 1 unit and y stays the same

b2

Select one:

y changes by 0.5412 when x1 increases by 1 unit and x2 stays the same

y changes by 0.5412 when x2 increases by 1 unit and x1 stays the same

x1 changes by 0.5412 when x2 increases by 1 unit and y stays the same

x2 changes by 0.5412 when x1 increases by 1 unit and y stays the same

Predict y when x1 = 180 and x2 = 310 (to 3 decimals).

Explanation / Answer

The regression coefficient of b1 here given is 0.5817, therefore for a unit change in X1, there would be an increase of 0.5817 units in the dependent variable y keeping X2 the same.

Therefore the correct answer here would be given as: y changes by 0.5817 when x1 increases by 1 unit and x2 stays the same

The regression coefficient of b2 here given is 0.5412, therefore for a unit change in X2, there would be an increase of 0.5412 units in the dependent variable y keeping X1 the same.

Therefore the correct answer here would be given as: y changes by 0.5412 when x2 increases by 1 unit and x1 stays the same

The predicted value here is computed as:

= 33.1848 + 0.5817x1 + 0.5412x2 = 33.1848 + 0.5817*180 + 0.5412*310 = 305.6628

Therefore 305.663 is the predicted value here.

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