Je suis un peu un novice dans l'économétrie et j'ai un petit problème dont je ne trouve pas les réponses (qui vous paraîtra surement triviale). Je n'y comprends rien...!

Pouvez-vous m'aider ?

Problem 1 : simple OLS regression

You run a simple regression of y on x, and find that the corresponding R2 is equal to 0,5.

1) Can the estimated coefficient of the regressor be equal to zero? And the constant term? 

2)Assume that the estimated coefficient of the regressor is equal to 1. Write down the variance of the fitted value . Is the variance of x greater or smaller than the variance of y?

3)If you were to add a second regressor to your model, would it be possible that the R2 goes down? Discuss the effect of adding that second regressor on the estimated coefficient of the first regressor according to the covariance between them.