looking through my notes, having a bit of trouble understanding it.
a) how do i get the values circled in red? (for the f-test)
b) how do i get the values circled in green? (for the t-test)
c) how do i come to the conclusion in blue? (value of F is significant at the 0.1% level)
d) how do i come to the conclusion for the t-test is significant at the 0.1% level?
e) What does 100(gamma) and gamma/2 mean? what is gamma?
So, for your values circled in Red: Those are the values that you get from the F distribution table. If you have a statistics textbook, the F distribution table is usually located in the back of the book. Also, if you have used any computer program R will spit out these same numbers. Example: for R, the code would be qf(1-.05, 1, 11).
The values in green are also obtained from the table. Based on the gamma/2, I am assuming you are doing a two sided test and that you have to divide the significance level by 2. For R, the code would be qt(1-(.05/2), df = 11).
The conclusion in Blue: I am assuming that you are testing at that particular significance level. So, If your F-stat > f critical value, then you reject the null hypothesis and conclude that the model you are using is a good one and that there is a strong relationship between your dependent and independent variables. Remember the criteria for rejecting the null and what that means once rejected or not.
The T test tests the significance of the dependent variable on the independent variable separately (the F tests the entire model). So, if |T| > t critical value, then you reject the null hypothesis and conclude that your tested variable is significant. So, in this case, there is evidence of a relationship between X and Y.
Gamma*100 is basically how confident you are in your answer and whatnot. Gamma is your confidence level, or your critical level. In the F case, your gammas are .05, .01, and .001. For your T, your gammas are the same thing but remember that when doing a Two sided t test, you have to divide your significance level (gamma) by two. I hope this helps.