Stor 155, Section 2, Last Time

1
Stor 155, Section 2, Last Time

• Inference for Regression
• Least Square Fits
• Sampling distribns for slope and intercept
• Regression Tool
• Gave many useful answers
• (CIs, Hypo Tests, Graphics,)
• But had to translate language

2
Reading In Textbook

• Approximate Reading for Todays Material
• Pages 634-667
• Next Time All review

3
Stat 31 Final Exam

• Date Time
• Tuesday, May 8,  800-1100
• Last Office Hours
• Thursday, May 3, 1200 - 500
• Monday, May 7, 1000 - 500
• by email appointment (earlier)
• Bring with you, to exam
• Single (8.5" x 11") sheet of formulas
• Front Back OK

4
Prediction in Regression

• Idea Given data
• Can find the Least Squares Fit Line, and do
  inference for the parameters.
• Given a new X value, say , what will the new
  Y value be?

5
Prediction in Regression

• Dealing with variation in prediction
• Under the model
• A sensible guess about ,
• based on the given ,
• is
• (point on the fit line above )

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Prediction in Regression

• What about variation about this guess?
• Natural Approach present an interval
• (as done with Confidence Intervals)
• Careful Two Notions of this
• Confidence Interval for mean of
• Prediction Interval for value of

7
Prediction in Regression

• Confidence Interval for mean of
• Use
• where
• and where

8
Prediction in Regression

• Interpretation of
• Smaller for closer to
• But never 0
• Smaller for more spread out
• Larger for larger

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Prediction in Regression

• Prediction Interval for value of
• Use
• where
• And again

10
Prediction in Regression

• Interpretation of
• Similar remarks to above
• Additional 1 accounts for added variation
  in compared to

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Prediction in Regression

• Revisit Class Example 33,
• Textbook Problem 10.23-10.25
• Engineers made measurements of the Leaning Tower
  of Pisa over the years 1975 1987. Lean is
  the difference between a points position if the
  tower were straight, and its actual position, in
  tenths of a meter, in excess of 2.9 meters. The
  data are listed above

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Prediction in Regression

• ??? Next time spruce up these examples a lot
  ???

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Prediction in Regression

• Class Example 33,
• Textbook Problems 10.23 10.25
• Plot the data, Does the trend in lean over time
  appear to be linear?
• What is the equation of the least squares fit
  line?
• Give a 95 confidence interval for the average
  rate of change of the lean.
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg33.xls

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Prediction in Regression

• HW
• 10.7 b, c, d
• 10.8 ((c) 11610, 12660, 9554, 14720)

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Prediction in Regression

• Revisit Class Example 33,
• Textbook 10.23 10.25
• Engineers made measurements of the Leaning Tower
  of Pisa over the years 1975 1987. Lean is
  the difference between a points position if the
  tower were straight, and its actual position, in
  tenths of a meter, in excess of 2.9 meters. The
  data are listed above

16
Prediction in Regression

• Class Example 33, Problem 10.24
• In 1918 the lean was 2.9071 (the coded value is
  71). Using the least squares equation for the
  years 1975 to 1987, calculate a predicted value
  for the lean in 1918
• Although the least squares line gives an
  excellent fit for 1975 1987, this did not
  extend back to 1918. Why?
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg33.xls

17
Prediction in Regression

• Class Example 33, Problem 10.25
• How would you code the explanatory variable for
  the year 2002?
• The engineers working on the tower were most
  interested in how much it would lean if no
  corrective action were taken. Use the least
  squares equation line to predict the lean in
  2005.
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg33.xls

18
Prediction in Regression

• Class Example 33, Problem 10.25
• (c) To give a margin of error for the lean in
  2005, would you use a confidence interval for the
  mean, or a prediction interval? Explain your
  choice.
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg33.xls

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Prediction in Regression

• Class Example 33, Problem 10.25
• Give the values of the 95 confidence interval
  for the mean, and the 95 prediction interval.
  How do they compare?
• Recall generic formula (same for both)

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Prediction in Regression

• Class Example 33, Problem 10.25
• Difference was in form for SE
• CI for mean
• PI for value
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg33.xls

21
Outliers in Regression

• Caution about regression
• Outliers can have a major impact
• http//www.math.csusb.edu/faculty/stanton/m262/reg
  ress/regress.html
• Single point can throw slope way off
• And intercept too
• Can watch for this, using plot
• And residual plot show this, too

22
Nonlinear Regression

• When lines dont fit data
• How do we know?
• What can we do?
• There is a lot
• But beyond scope of this course
• Some indication

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Nonlinear Regression

• Class Example 34 World Population
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg34.xls
• Main lessons
• Data can be non-linear
• Identify with plot
• Residuals even more powerful at this
• Look for systematic structure

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Nonlinear Regression

• Class Example 34 World Population
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg34.xls
• When data are non-linear
• There is non-linear regression
• But not covered here
• Can use lin. regn on transformed data
• Log transform often useful

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Next timeAdditional Issues in Regression

• Robustness
• Outliers via Java Applet
• HW on outliers

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And Now for Something Completely Different

• Etymology of
• And now for something completely different
• Anybody heard of this before?
• (really 2 questions)

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And Now for Something Completely Different

• What is etymology?
• Google responses to
• define etymology
• The history of words the study of the history of
  words.csmp.ucop.edu/crlp/resources/glossary.html
  
• The history of a word shown by tracing its
  development from another language.www.animalinfo.
  org/glosse.htm

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And Now for Something Completely Different

• What is etymology?
• Etymology is derived from the Greek word
  e/)tymon(etymon) meaning "a sense" and
  logo/j(logos) meaning "word." Etymology is the
  study of the original meaning and development of
  a word tracing its meaning back as far as
  possible.www.two-age.org/glossary.htm

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And Now for Something Completely Different

• Google response to
• define and now for something
• completely different
• And Now For Something Completely Different is a
  film spinoff from the television comedy series
  Monty Python's Flying Circus. The title
  originated as a catchphrase in the TV show. Many
  Python fans feel that it excellently describes
  the nonsensical, non sequitur feel of the
  program. en.wikipedia.org/wiki/And_Now_For_Someth
  ing_Completely_Different

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And Now for Something Completely Different

• Google Search for
• And now for something completely different
• Gives more than 100 results.
• A perhaps interesting one
• http//www.mwscomp.com/mpfc/mpfc.html

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And Now for Something Completely Different

• Google Search for
• Stor 155 and now for something completely
  different
• Gives
• PPT Slide 1
• File Format Microsoft Powerpoint - View as
  HTMLhttp//stat-or.unc.edu/webspace/postscript/ma
  rron/Teaching/stor155-2007/ ... And Now for
  Something Completely Different. P Dead bugs on
  windshield. ...stat-or.unc.edu/webspace/postscrip
  t/marron/Teaching/stor155-2007/Stor155-07-01-30.pp
  t - Similar pages

32
Review Slippery Issues

• Major Confusion
• Population Quantities
• Vs.
• Sample Quantities

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Review Slippery Issues

• Population Mathematical Notation
• (fixed unknown)
• Sample Mathematical Notation
• (summaries of data, have numbers)

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Hypothesis Testing Z scores

• E.g. Fast Food Menus
• Test
• Using
• P-value Pwhat saw or m.c. H0 HA bdry
• (guides where to put 21k 20k)

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Hypothesis Testing Z scores

• P-value Pwhat saw or or m.c. H0 HA bdry

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Hypothesis Testing Z scores

• P-value
• This is
  the Z-score
• Computation Class E.g. 24, Part 6
• http//stat-or.unc.edu/webspace/postscript/marron/
  Teaching/stor155-2007/Stor155Eg24.xls
• Distribution N(0,1)

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Hypothesis Testing Z scores

• P-value
• So instead of reporting tail probability,
• Report this cutoff instead,
• as SDs away from mean 20,000

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Review for Final

• An Important Mode of Thinking
• Ideas vs. Cookbook

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Ideas vs. Cookbook

• How do you view your sheet of formulas?
• A set of recipes?
• Look through list to solve problems?
• Getting harder to find now?
• Problems
• Too many decisions to make
• Hard to sort out while looking through

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Ideas vs. Cookbook

• Too many decisions to make, e.g.
• Binomial vs. Normal
• 1-sided vs. 2-sided Hypo. Tests
• TDIST (INV) vs. NORMDIST (INV)
• CI vs. Sample Size calculation
• 1 sample vs. 2 sample
• Which is H0, HA? And what direction?
• What is m.c.? What is Bdry?

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Ideas vs. Cookbook

• Suggested Approach
• Use concepts to guide choice
• This is what I try to teach
• And is what I am testing for
• How to learn?
• Go through old HW (random order)
• When stumped, look through notes
• (look for main Ideas, not the right formula)

42
A useful concept

• Perhaps not well taught?
• a b - Number of spaces between a and b
  on the numberline
• e.g. Midterm II, problem 3c (x 0, 1, 2, 3)
• X 1 gt 1 number of spaces between X
  and 1 is more than 1
• X 3

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A useful concept

• e.g. Midterm II, problem 3c (x 0, 1, 2, 3)
• X 1 gt 1 number of spaces between X
  and 1 is more than 1
• X 3
• Because
• 0 1 2
  3

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Response to a Request

• You said at the end of today's class that you
  would be willing to take class time to "reteach"
  concepts that might still be unknown to us.
• Well, in my case, it seems that probability and
  probability distribution is a hard concept for me
  to grasp.
• On the first midterm, I missed and on the
  second midterm, I missed
• I seem to be able to grasp the other concepts
  involving binomial distribution, normal
  distribution, t-distribution, etc fairly well,
  but probability is really killing me on the
  exams.
• If you could reteach these or brush up on them I
  would greatly appreciate it.

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A Flash from the Past

• Two HW Traps
• Working together
• Great, if the relationship is equal
• But dont be the yes, I get it person
• The HW Consortium
• You do HW 1, and Ill do HW 2
• Easy with electronic HW
• Trap HW is about learning
• You dont learn on your off weeks