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Lecture 5, 2018/09/28:

RECAP:

- Make the first and second order assumptions for a linear model
  with response vector y (nx1) and regressor matrix X (nx(p+1)).
  Let R be an orthogonal NxN matrix and let z = R y.
  What kind of model do you get for the vector z as the response?
  What are the vectors of OLS coefficient estimates, fitted values, residuals?

- Geometrically, what is the meaning of "degrees of freedom"?

- Statistically, what do "degrees of freedom" tell you about
  total variances?

- If you add one more regressor to your regression,
  what happens to the variability (total variance)
  of the vectors of fitted values and residuals?

- Do degrees of freedom depend on whether you added a good or
  a bad regressors?

- Is it true that  E[RMSE] = sigma  ?  Yes / no?

- Derive the proper unbiasedness property.

- Is it desirable?  If yes, why.  If no, why not?

- In the derivation of this property, what assumptions did you use?

- Recall the 1st and 2nd order properties of the OLS estimate.

- How can you see that the OLS estimate gets more precise
  with more data point?

- What happens to the self-influence value H_11 as n --> Inf?


ROADMAP: Regression adjustment and its applications



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Lecture 4, 2018/09/21:

RECAP:

- Quiz 1 review

- What is the range of the hat diagonal elements H_ii ?

- Self-influence?

- Budget consideration of V[r_i] vs V[yhat_i] ?

- Definition of trace?

- Trace of H ?

- Total variance?

- Budget considerations for total variance of r vs yhat?


ROADMAP:

- Estimating sigma^2

- Long-run properties of the X matrix

- Interpretation of the hat matrix diagonal as measure of outlyingness

- Regression adjustment

- Application 1 of adjustment: centering

- Application 2 of adjustment: reduction of multiple to simple regression


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Lecture 3, 2018/09/14:

ORG:
- Next time (9/21) there will be a short quiz at the beginning of class.


RECAP:


* OLS Estimates: betahat, yhat, residuals

  ...


* Linear models assumptions, 1st & 2nd order:

  ...


* Vector random variables / random vectors, 1st & 2nd order properties

- Definitions:

  . 1st order moments:

      ...

  . 2nd order moments:

      ...

- What kind of averaging is going on in E[...] and V[...]
  in regression?

      ...


- 1st order properties under affine operations:

  ...


- 2nd order properties under affine operations:

  ...


* 1st & 2nd order properties of betahat:

  ...
  ...



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Lecture 2, 2018/09/07:

ORG:
- This class has just one purpose...


RECAP:

REMEDIAL R
- Basic atomic data types and their purposes:
  .
  .
  .
  .
- Missing value types and their algebra:
  .
  .
  .
  .
- Composite data types and their purposes:
  .
  .
  .
  .
- Types of indexed vector/matrix/array/dataframe access:
  .
  .
  .
  .
- Concepts:
  . High vs low level languages: characteristic and examples
      Low:
      High:
  . Coercion: ...
      Examples:
        What is the sum and the mean of a logical vector?
          x <- runif(100)<0.25
          sum(x)
          mean(x)
  . Hash tables: What are they and where are they in R?  ...
  . Recycling: What is it?
        cbind(1:10, 1:2)
        cbind(1:10, 1:3)   # What is different?
        paste(c("A","B"), letters, sep="")
        matrix(c("+","-"), nrow=5, ncol=5)
- Loops:
    good and bad uses
- Regular expressions:
    what are they?
- Plotting:
    Invest in fine-tuning plots for your papers.
    Don't waste space (base-R plots have wasteful defaults)
    Don't allow plot content to bleed into the border (base-R plots do bleeding)

BABY INFERENCE:
- What is the meaning of "variability" in estimates of a mean?  median?  standard deviation?
- What is the meaning of probability when applied to estimates?
- What is the difference between standard deviation and standard error?
- What makes mean and max so different as estimates?
- What is the relation between retention intervals of statistical tests (RIs)
    and confidence intervals (CIs)?

ROADMAP:
- Finish baby inference
- Next: Basics of linear models (half-hearted)