Question: Suppose you have these observations on x and y:

Calculate (manually): \[\]

i) \(\bar{X}\) and \(\bar{Y}\)

ii) \[{{\hat{\beta }}_{0}}\] and \[{{\hat{\beta }}_{1}}\] if you hypothesize that x and y are related (in the population) in the following manner:

You need to use the formulas for calculating the parameters, not SAS or Stata.

iii) SST, SSR, SSE, R²

iv) Show that the residuals add to zero.

Note: Please show all the steps.