# Statistics: Hypothesis Testing – #245

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

 x Y 0 3 1 6 2 5 3 8 4 9 5 13

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:

E(y|x) = β0 + β1x

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.

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