Question

In the model Yi = β0 + β1X1 + β2X2 + β3(X1 × X2) + ui, suppose X1 increased by 1 unit, then expected effect for Y is (How much Y will increase?):

A. β1.

B. β1 + β3X2.

C. β1 + β3X1.

D. β1 + β3.

The interpretation of the slope coefficient in the model ln(Yi) = β0 + β1 ln(Xi)+ ui is as follows:

A. a 1% change in X is associated with a change in Y of 0.01 β1.

B. a change in X by one unit is associated with a 100 β1 % change in Y.

C. a change in X by one unit is associated with a β1 change in Y.

D. a 1% change in X is associated with a 100β1 % change in Y.

Diogenes was asked concerning paintings of those who had escaped shipwreck: "Look, you who think the gods have no care of human things, what do you say to so many persons preserved from death by their especial favor?", to which Diogenes replied: "Why, I say that their pictures are not here who were cast away, who are by much the greater number." What kind of internal invalidity did Diogenes think the original question suffered from?

A. Sample Selection Bias

B. Omitted Variable Bias

C. Errors-in-Variables Bias

D. Simultaneous Causality Bias

Answer 1

Yi = 0 + 1 X1 + 2 X2 + 3 ( X1 * X2 ) + Ui

Ans . 1 + 3 X2
Reason : Suppose X1 is 0 , Then
Yi = 0 + 1 X1 + 2 X2 + 3 ( X1 * X2 ) + Ui
= 0 + 1 (0) + 2 X2 + 3 ( 0 * X2 ) + Ui
= 0 + 2 X2 + Ui
Now , X1 is increased by 1
So X1 = 0 + 1 = 1
At X1 = 1 ,
Yi = 0 + 1 X1 + 2 X2 + 3 ( X1 * X2 ) + Ui
= 0 + 1 (1) + 2 X2 + 3 ( 1* X2 ) + Ui
= 0 + 1 + 2 X2 + 3 X2 + Ui

Increase in Yi when X1 increases by 1 is :
New Yi - Old Yi
= [ ​​​​​​​0 + 1 + 2 X2 + 3 X2 + Ui ] - [  0 + 2 X2 + Ui ]
= 1 + 3 X2

Thus when X1 is increased with 1 unit then Y will increase with  ​​​​​​​1 + 3 X2 units.

Sorry, I am legally bound by answering limit.
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