E(X(x-1)) is a 2nd factorial moment. Finding the factorial moment for rv~ poisson proved 2 ways - using the probability generating function of a poisson; directly from expectation of a function of a random variable ... https://www.youtube.com/watch?v=a2MGE3olzwA
It's easier to work with the cumulant generating function cgf than the moment generating function in cases where it's easier to differentiate the cgf than the mgf. The first derivative of the cgf is the mean, the second derivative of the cdf is the variance of the random variable.
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https://www.youtube.com/watch?v=OYhfMRAf_zQ
OLS for standard multiple linear regression example
Econometrics/statistics questions and answers
0:33 inverse of X'X (the Gram matrix)
5:06: Handy tips
- by looking at X we can tell how many observations there are, and how many unknown parameters, and whether or not an intercept is in the model
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https://www.youtube.com/watch?v=2Ma7w7F_50M
Pictures used to introduce the cobweb model. Don't worry - I don't do any algebra (although that doesnt mean I don't write down any equations!). Supplement to stuff we did in class. If it's going to convince you to watch this video, let's say I cover more here than I did in class on this topic.
What is the cobweb model?
How does the cobweb model work?
Can you show me a graph of how prices and quantity reach equilibrium over time in a cobweb model?
Does the cobweb model always get me to the market equilibrium price and quantity?
What are the equations for a cobweb model?
What conditions ensure the market equilibrium is stable for the cobweb model with linear supply and demand sets?
What happens when the conditions for market to be stable doesn't hold for the cobweb model?
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https://www.youtube.com/watch?v=4toy6f6huCQ
Simple linear (bivariate) regression on a subset (part of) of the data; getting more than 1 plot in a window; extraction of a subset of the data.
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https://www.youtube.com/watch?v=LeqsaIX7XkI
T-test in multiple linear regression for testing individual significance
1:15 Steps in testing the significance of a slope parameter
4:40 Things to watch out for
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https://www.youtube.com/watch?v=rt72lB09eGs
How to add bands at +/-2 times the standard deviation of the residuals on the residual plot. These bands are to help identify any regression outliers.
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https://www.youtube.com/watch?v=ztbHqy138dQ
I fitted a regression where Y was skewed,
but the residuals came out normal. How can this be?
Isn't it an assumption that the Y must be normally distributed
for the residuals to be normal too?
Mariachi Snooze by Kevin MacLeod is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100166
Artist: http://incompetech.com/
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https://www.youtube.com/watch?v=1ft8v7PlNKQ
GLM with Bernoulli response. Likelihood function for mle, score function, and information matrix for logistic regression for ungrouped data. In this question the canonical link - the logit function - is used.
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https://www.youtube.com/watch?v=WzWxI3-5psw