I got phi-rat=0.542508. standard error=((1-0.542508^2)/8)^0.5=0.297

T-value for 95% and 8 freedom is equal to 2.306,

so, confidence interval is (0.542508-0.297*2.306,0.542508+0.297*2.306
)=(-0.14238,1.227398).

I have a question on how the standard deviation should be calculated. Using the formula on page 41, I calculate the standard deviation as s=((sum(Yt-phi)^2)/8)^.5. This however does not get me close to the standard deviation I get from my excel analysis (0.27476412), it got me to 0.653814. I don’t understand the assumption that the standard error is =((1-0.542508^2)/8)^0.5=0.297. Where does this formula come from?

I have no idea how to manually get the standard error found by excel (.289466).  If anyone has an idea how to get this I would appreciate any help.

Note: We are using 6 degree's of freedom when calculating the t value?  That is the only way for me to match the confidence intervals using excels standard error.

I assume this is because we had 8 entries (or rather pairs of Y_t and Y_t-1) and estimated 2 parameters, correct?

Thanks for any clarification.

This would be a lot easier to understand if you have already taken the Regression Analysis Course.

Basically, SE(phi) = sqrt( (RSS / n-2) / sum(X* ^2) )
where n = the no. of observations (so yes, you are correct in supposing that degrees of freedom = 6 = 8-2)

RSS = the sum of the squares of the differences between Y and the fitted Y from the regression
--> Using the first observation (X = 0.44, Y = 1.05), the fitted Y is computed as follows:
fitted Y = the intercept from the regression (0.585417) + the estimated phi (0.542508) * X (0.44) = 0.82412

--> Then (Y - fitted Y)^2 = (1.05 - 0.82412)^2 = 0.051022

Do this for all observations and get the sum, which would be the RSS.

X* ^2 = (X - average of all the X's)^2
e.g. for the first observation, this would be (0.44 - 0.99)^2 = 0.3025
Then do this for all observations yet again and get the sum.



I hope this makes sense to you.