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We believe that the population relation is described by the following equation:
y = β0 + β1x + E (1)
Imagine that we believe that Assumption 4 (the unconditional mean zero assumption) is not satisfied. Show that one can find an equation that also describes the relation in the population between y and x and that does satisfy Assumption 4.
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We have the following population model:
y = β0 + β1x + E
We have to decide between two alternative estimators. The density functions of the two estima- tors are displayed below. Discuss briefly which estimator you prefer.
We have studied the effect of the NTV TV station coverage on the percentage of votes that the party supporting Vladimir Putin received in the 1999 Duma elections. We obtained the STATA output below:
Compute the slope coefficient that we would have obtained if we had run a simple regression of
votesPutin on NTV.
Question 7: We believe that, in the population, the relation between y and x is negative. Unfortunately, our sample was not obtained randomly, but instead it contains only observations with a value of y below a certain threshold. Explain graphically whether the error term in our model is positively or negatively correlated with our independent variable x.
X and Y are independent random variables.
We wanted to understand the relation between journal demand and the lightness of the journal covers. In order to do that, we ran the following regression:
where we have standard errors in parentheses. Our sample size is 180. Test the null hypothesis that the effect is zero against the alternative hypothesis that the effect is negative at the 5% level.
Question 9: We wanted to estimate the returns to education separately for every state in the US. Our population model is:
For every state we used a sample size equal to 1/100,000 of the state population. The table below displays the estimated coefficients for ten states: