(Solved): Consumption data for 22 individuals produce the following (where y=log (consumption) and x=log( inc ...

Consumption data for 22 individuals produce the following (where $y=\log$ (consumption) and $x=\log ($ income $))$ : $\begin{array}{l}\stackrel{?}{y}=20,\\ {?}_t{y}_t^2=8900,\\ \stackrel{?}{x}=10,\\ {?}_t{\left(x_t?\stackrel{?}{x}\right)}^2=60,\\ {?}_t\left(x_t?\stackrel{?}{x}\right)\left(y_t?\stackrel{?}{y}\right)=30\end{array}$ where $\stackrel{?}{x},\stackrel{?}{y}$ are the sample means of $\mathrm{x}$ and $\mathrm{y}$. 1. Compute the least squares estimates of $?,?$ in the model: $y_t=?+?x_t+u_t$. 2. Test the hypothesis that $?=1$ (assume that $u_t$ is i.i.d. and normally distributed). 3. Compute the centered $R^2$.