Stats Solutions

[Solution] Consider the data in the following table: i 1 2 3 4 5 6 7 8 9 10 xi 1 1 1 2 2 2 3 3 3 20 yi 1 2 3 1 2 3 1 2 3 20 Find the sample correlation coefficient

Question: Consider the data in the following table:

i 1 2 3 4 5 6 7 8 9 10
xi 1 1 1 2 2 2 3 3 3 20
yi 1 2 3 1 2 3 1 2 3 20
  1. Find the sample correlation coefficient r.
  2. Show that test statistic \[t={{\hat{\beta }}_{1}}/({{S}_{y!x}}/{{S}_{x}}\sqrt{n-1})\] for testing \[{{H}_{\circ }}={{\beta }_{1}}=0\] (based on a straight line regression relationship between y and x) is exactly equivalent to the test statistic of \[t=r\sqrt{n-2}/\sqrt{1-{{r}^{2}}}\] for testing H 0 : ρ=0
  3. Using the latter t , test H 0 : ρ=0 versus H A : ρ≠ 0

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Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document


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