Interpretations

Question 1

β1 interpretation

Answer 1

-> 1. Univariate: is the mean value of Yi when the value of explanatory variable Xi is zero;
-> 2. Multivariate: is the mean value of Yi when the value of ALL explanatory variables is zero;

Question 2

(β2) … (βk) interpretation

Answer 2

-> 1. Univariate: is the average variation of the mean value of Yi in the presence of unit variations of explanatory variable Xi.
-> 2. Multivariate: the average variation of the mean value of the endogenous variable in the presence of unit variations of (X2)… (Xk), with all other explanatory variables remaining constant (“ceteris paribus” clause).

Question 3

β1 estimated, interpretation

Answer 3

-> 1. Univariate: It is the estimated mean value of Yi when the value of explanatory variable Xi is zero.
-> 2. Multivariate: It is the estimated mean value of Yi when all explanatory variables are equal to zero.

Question 4

(β2) estimated … (βk) estimated, interpretation

Answer 4

-> 1. Univariate: Estimated average variation in the estimated mean value of Yi in the presence of unit changes in explanatory variable Xi;
-> 2. Multivariate: Estimated average variation of the estimated mean value of the endogenous variable in the presence of unit variations of (X2)…(Xk), with all other explanatory variables remaining constant (“ceteris paribus” clause).

Question 5

Elasticity

Answer 5

A 1% increase in X2i causes an estimated “mean” increase of ?% in the estimated mean of Yi, keeping all other variables constant.