Is it true that for simple regression, tstat = r(squrt(n-2)) / (squrt(1-r^2)) and for multiple regression, tstat = (b1-null)/stderror? If true, does this mean that if we are given a table and there is only an intercept and one independent variable, that we should use the first tstat formula above (with the r’s)?
the hint on those sorts of q’s- they’ll give you a correlation where as most of the time they don’t. when they do, dial this formula up from your memory banks.
OK, the first formula is to test the significance of “r” itself - whether there is indeed any correlation between indep. and dep. variable. This is for simple regression. I don’t think it’s true for multiple regression. The second formula is for the coefficients - to test whether a given coefficient differs significantly from 0. This one is the same for multiple and for simple regression.
ok naze i think youre right. on quicksheet for the first formula it says “t-test for r”. so if they ask if correlation is significant, you use this formula which gives you youre tstat, find the tcritical values using t-tables, and find if it’s significant with your null being that correlation =0. and then the second formula is the one were accustomed to using in hypothesis tests, and we would use it to test for things like hetero, autocorrelation, and multicoll… this good with you?
Both of these statistics are used for hypothesis testing. The first one is used to (try to) reject the H_0: correlation = 0. If you can reject that, then there’s correlation between ind. and dep. variable (ie correlation is > 0). The second one is used to (try to) reject the H_0: coefficient b = 0. If you can reject that, then the coefficient b is different from 0. (and the corresponding variable serves to explain a part of the dependent variable). The second one is not used to test for heterosked, autocorrelation or the like. Off the top of my head, you use the Breusch Pagan test for heterosked, Durbin Watson for autocorrelation.
ok i see. thank you.