Thanks for the lecture :) In the assumption (22:00), y ~ N(y-hat, std of residual) is mentioned. >> I found it weird X doesn't have any contribution in the variance of Y. Is it because explanatory variables are controlled, such that var(X) = 0 ? (or let's say X is not treated as a random variable) However, assume we have some X's set at 1 volt, 2 volts and 3 volts for example. We can still calculate the variance with those numbers. In this case, the variance will not be zero, [(1-2)^2+(2-2)^2+(3-2)^2] / 3 = 2/3. Also, in the review courses, the confidence interval of the coefficient can be given by their variances, which contain 1 / var(X) in the formula. Then how can we construct the interval if Var(X) = 0 or it's not treated as a random variable? Thanks again.
I list of couple of optional books to go with the course on the course website: www.lithoguru.com/scientist/statistics/. In general, I like everything written by Douglas Montegomery.
![[TF2] The Russian Bear Trap](http://i.ytimg.com/vi/YFNSwz2_rOA/mqdefault.jpg)
A PDF copy of all the slides in this course (and other material) are available at:
www.lithoguru.com/scientist/statistics/course.html
Thanks for the lecture :)
In the assumption (22:00), y ~ N(y-hat, std of residual) is mentioned.
>> I found it weird X doesn't have any contribution in the variance of Y.
Is it because explanatory variables are controlled, such that var(X) = 0 ? (or let's say X is not treated as a random variable)
However, assume we have some X's set at 1 volt, 2 volts and 3 volts for example. We can still calculate the variance with those numbers.
In this case, the variance will not be zero, [(1-2)^2+(2-2)^2+(3-2)^2] / 3 = 2/3.
Also, in the review courses, the confidence interval of the coefficient can be given by their variances, which contain 1 / var(X) in the formula.
Then how can we construct the interval if Var(X) = 0 or it's not treated as a random variable?
Thanks again.
Thank you, Chris, for your time and effort!! do you recommend a reference book for studying Statistics?
I list of couple of optional books to go with the course on the course website: www.lithoguru.com/scientist/statistics/. In general, I like everything written by Douglas Montegomery.
@@ChrisMack Thanks a lot :)
Making this course online-available is much appreciated :)
Are we assuming the variance of the error is equal to 1?
No. We just assume that the variance of the error is the same for every data point.