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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