Question: (5 points) True or false. If false, please explain.

Suppose there is a sample from the population \(y={{\beta }_{0}}+{{\beta }_{1}}x+u\). The sample size is n. The corresponding OLS estimation function is \(\hat{y}={{\hat{\beta }}_{0}}+{{\hat{\beta }}_{1}}x\). Then,

1. \(y=\alpha +\beta \frac{1}{x}+u\) is nonlinear.
2. \(E\left( u \right)=0\)
3. \({{\hat{\beta }}_{1}}={{\beta }_{1}}\)
4. OLS estimation is trying to minimize \(\sum\limits_{i=1}^{n}{\left( {{y}_{i}}-{{{\hat{y}}}_{i}} \right)}\)
5. \(E\left( {\hat{u}} \right)=0\)

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