I show the formulas (and work through some of the underlying logic) for confidence intervals and hypothesis tests on the slope parameter in simple linear regression.
I love how you actually describe what EACH term and variable means for an equation and how removing them or adding them effects our final value. If only more math was taught this way. Great example in the video here is how you told us that we use n-2 because we have lost 2 degrees of freedom when estimating our parameters. And then you told us WHICH degrees of freedom we lost, specifically. Man you just don't know how good it feels for the blinders to fall off this way. Thank you, so much and your understanding of things will help us with EVERY OTHER math problem we face in the future.
I'm almost done with my MS in statistics and have learned all these things, but I still really enjoy watching your videos here and there as they're always good refreshers and so clearly explained. You're an excellent educator. :)
That is so useful. I have been wondering about why we have to use n-1 in the denominator for the sample standard deviation when approximating the population standard deviation. We proved this mathematically in our courses. But the way that you summarize things up on a higher level is just coooooooooooooooool.
Same idea as for any statistic. Yes, once we get a sample and calculate its value, it'll be a value. Until then it's a theoretical notion that has a distribution (a random variable). If we took a different sample, we'd get a different value. Introduction to the concept of sampling distributions: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Zbw-YvELsaM.html&ab_channel=jbstatistics
@@letseconomics2938 That sort of thing, yes. The value of beta_1 hat that we see in any given sample can be thought of as a random sample from that distribution. We use (estimated) characteristics of that distribution in our inference procedures.
