Consider a sample of 32 observations on variables X and Y in which the correlation is 0.30. If the level of significance is 5%, we: A) conclude that there is significant correlation between X and Y. B) cannot test the significance of the correlation with this information. C) conclude that there is no significant correlation between X and Y. Answer is: The calculated t = (0.30 × Sq Root of 30) / Square root of 1- 0.09) = 1.72251 and the critical t values are ± 2.042. Therefore, we fail to reject the null hypothesis of no correlation. I get everything else but how did they get the R2?
0.30^2?
Thats not needed anywhere in this example. You’re testing if there is a positive co-relation between x and y. all you need is the r ( Co-relation coefficient ) and n ( Sample Size ).
deepstack31 Wrote: ------------------------------------------------------- > Thats not needed anywhere in this example. You’re > testing if there is a positive co-relation between > x and y. > > all you need is the r ( Co-relation coefficient ) > and n ( Sample Size ). you need r^2 to get the T-stat in this case don’t you?
The formula for the t stat, to test co-relation is r * ( n -2) ^ 0.5 divided by : ( 1-r ) ^ 0.5 this is one of the first topics in quant, and you’re testing co-relation coefficient here, not the significance of the slope coeffcient.
I think you have the formula wrong, I know it as (as does the formula sheet): r*(n-2)^.5 divided by: (1-r^2)^.5
Yes. you’re right. My bad. Though thats just the square of r, not R Squared ( the thing that we get from Anova Table). Although for 2 variables it amounts to the same thing.
exactly, the only reason why it’s confusing. thanks Deepstack