a. Using algebra, establish an alternative expression

\[b_{1}=\frac{\sum_{i=1}^{n} \text { weight }_{i} \times \text { slope }_{i}}{\sum_{i=1}^{n} \text { weight }_{i}} .\]

Here, slope \(_{i}\) is the slope between \(\left(x_{i}, y_{i}\right)\) and \((\bar{x}, \bar{y})\). Give a precise form for the weight weight \(i\) as a function of the explanatory variable \(x\).

b. Suppose that \(\bar{x}=4, \bar{y}=3, x_{1}=2\) and \(y_{1}=6\). Determine the slope and weight for the first observation, that is, slope \(_{1}\) and weight \(_{1}\).