Consider the data in the following table: i 1 2 3 4 5 6 7 8 9 10 xi

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

a) Find the sample correlation coefficient r.

b) 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 H₀ : ρ=0

c) Using the latter t , test H₀ : ρ=0 versus H_A : ρ≠ 0

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