Question: [14 Marks]

1. Consider the following model: \(Y={{\beta }_{1}}{{X}^{{{\beta }_{2}}}}\exp \left( e \right)\).
   As it stands, is this a linear model? If not, what "trick," if any, can you use to make it a linear regression model? Show your working
2. Suppose you are interested in estimating the relationship between advertisement expenditure (x) and sales (y): \(y={{\beta }_{1}}+{{\beta }_{2}}x+e\) . Consider the following five observations (in millions):

1. Compute \(\sum{\left( {{X}_{i}}-\bar{X} \right)\left( {{Y}_{i}}-\bar{Y} \right)}\), \(\sum{{{\left( {{X}_{i}}-\bar{X} \right)}^{2}}}\) and \(\sum{{{\left( {{Y}_{i}}-\bar{Y} \right)}^{2}}}\).
2. If the estimated intercept and slope coefficients are b ₁ = -3.10 and b ₂ =1.98 respectively, compute the residual series e. Interpret the regression coefficients
3. Compute SSE, SSR and SST.

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