Math 151 , Fall '07, Day 13 Fri. Sept 21 (autumnal equinox?)Hit reload.. .After class small correction to optional

HW Day 13 (Re)Read Ch. 4 (Scatterplots and correlation) to p. 99 Check p.105 4.12, 13, 14,   and Ahead pp. 99-105 (correlation) Check 4.14 thru 4.20.  You do not have to be able to calculate r by hand.  You should be able to guess roughly at an r for a swarm of data; as p.102, eg. 4.6, and know and  be able to use facts 1-4, p. 101, and cautions 1-4 p. 103.
Hand in Mon.
Scatterplots: 
p. 108, 4.24 date heights Make the scatterplot by hand.  Answer these questions instead of the ones given:  Describe the relationship--form, direction, strength,  (with only 6 points there's not enough data  to talk about outliers).  Is there any female dating a male shorter than she is?  (Keep a copy of the graph, to use in later work.)
p. 107 4.23 reading ability
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Scatterplots using SPSS.  Get Scatterplot handout, outside my door, or. pp.1-3, p.4
---From now on, make all scatterplots on SPSS!  Don't forget to check Measure, and to add Labels.  (Trouble printing? Try copy/paste into Word, printing in Word.  If you print from Word, on a computer without SPSS, symbols may look funny.  'S OK.)
SPSS Scatterplot Handout:  Use the handout and govsal_vs_pay.sav  data file to use SPSS and answer questions 1-5 (page 3 of handout).   Do Handout questions on a separate page, and Keep till we have finished all 12 questions!
p. 96, 4.4 and 4.5 (SPSS) bird colonies (Save your file; you'll use it again for 4.10)
p.96, 4.6 (SPSS) gas mileage
p. 98 4.7 (SPSS) icicle growth. Data is in table 4.2. Be sure to write on your graph which group is slow water and fast.
p. 109 4.25 a, c (not b) (SPSS) running records, M/F These are record breaking times, so a year without a number is one in which the best time was slower than the last record.  (Keep a copy of the graph, to use in the next section.)

- -.Postpone all Correlation. - - - - - - - - - - - - - - - 
Correlation (thinking):
p. 112, 4.36 and 4.37 Applet explorations
p. 112, 4.34 and 4.35 correlation meaning

4.26 date heights again  You graphed this by hand.  r = .5653. Now answer the questions in the text.

p. 109 4.25 b  running records again.  It's a little complicated in SPSS to get the r's for the separate groups, so get them by looking at the answers in the back of the book.  Answer the question.

A.  If women always married men who were exactly  two years older than themselves, what would be the correlation between the ages of husband and wife? (Hint: make  a data table and the corresponding scatterplot for 4 or 5 couples with different x's, and look at it.)

Correlation (computing & thinking)
SPSS Scatterplot Handout: Do problem 6, p. 3.  Keep this with the previous work.

p. 104, 4.11 (SPSS) gas, speed: association but 0 correlation.  Find the means and draw the mean lines on your graph (by hand) to help explain the 0 correlation.

p. 104, 4.10 (SPSS) bird colonies again.  To add a data pair in SPSS just type them in a new row at the bottom.  To delete, click on the case number, which highlights the whole row, hit delete.

(This problem looks forward to Ch. 5, sort of) 
 p. 110, 4.28 corn plant density. (SPSS)  Notice how the data is entered for SPSS--not as displayed here! but with the first column giving Plants per acre and the second giving Yield.  Make a scatterplot.  Use your calculator to find the mean yields. and write these on your paper. .  (Or You can find means for the separate groups in SPSS : in Explore, Plants to the Factor list).  Graph the means by hand with a pencil on your printed plot, and connect the means dots.

Read to discuss
Postpone
Correlation:
p. 112, 4.33  Do a rough sketch for yourself.

Look at all the graphs you make, and guesstimate the correlation coefficient (before you read or calculate it.)

Optional 
Do now (for ch. 5!) if you need the practice:
Straight line graphing practice:
A.  y = -10 + 3x, graph for 2<x<10.
B.  y = 500 - 20x, graph for 0<x<10.
 

 

- - - - .Postpone Correlation.
Correlation:  Use
http://www.whfreeman.com/bps4e, 
(see below for details) 
to make different scatterplot 
patterns, and observe their r's.

4.28, I said to draw the line by hand.
SPSS can plot the line
 connecting means
 on your graph:
 Get in Edit mode, do, Insert>Summary>Dot-Line.
The dots for the means are too much like the data dots. 
Do Format>Graph Elements>Line, and change them.

Exam1 returned:   Comments and solutions     Solutions

SPSS comments. 1) More is not better. Snowstorms of graphs and tables are not the point. Make the one graph (or 2) that address the issue. Find and mark, or copy, only the summary values you need. Discuss. Don't throw in un-discussed or irrelevant stuff.
2) What goes wrong with scale (quantitative) data labeled categorical in the Measure column? Solutions, p. 2 The numbers become just labels; the ruler line becomes a list of labels. Check every data set for this!

What happens further out in normal tails?  Almost (but not quite) 0.

Homework questions? Day 11    Day 12
   

Relationships:  (BPS4e, Ch. 4) Day 12
Timeplots:  are scatterplots, where the x axis shows time. (often a lurking variable: plot data against order of taking observations)
Handout on SPSS Scatterplots etc. p.1-3, p.4 , showing subgroups, labeling individual points.
govsal_vs_pay.sav  is the file used for most of the handout. (In SPSS for Class BPS folder)

Start here Monday:
Correlation:  The (Pearson) correlation coefficient r is a numerical measure for how strongly linear (and in what direction) the relationship is.  Doesn't substitute  for a scatterplot.
Use if data is:  2 quantitative variables, & "nice":
    One cluster/cloud/band.
   Pretty straight.
   Outlier(s)? Do with/without & be cautious.

Correlation experiments:  Website,  http://www.whfreeman.com/bps4e,"Statistical Applets",  Correlation/Regression.  Play with data points, observing the Correlation Coefficient.   Check in the "Show Mean X & Mean Y lines" box.  See how much is in each quadrant. Compare with correlation coefficient.

Using SPSS (p.4, Scatterplot handout) Analyze>Correlate>Bivariate

Properties (p. 101) and cautions (p. 103):

  1. Measures relationship--same whichever variable is on the x-axis
  2. "Unitless"--original measurment units (cm., inches) are "standardized out"
  3. Sign of correlation coefficient matches direction of relationship. + positive, -negative.
  4.  Between -1 and +1.   0: no linear relationship,   +1 or  -1: perfect straight line.
  1. Between two quantitative variables only!
  2. Does NOT give info about curved relationships (only measures linear part of relationship).
  3. NOT resistant to outliers--quite sensitive.
  4. Not a complete summary, even for nice linear data.  Need means, s.d.'s too.
correlation graph


--You won't have to calculate a correlation coefficient by hand. This formula is a bad one for hand computation (roundoff error); if you must do one by hand, find the computational formula in an old textbook.
--Eyeballing:  sketch xbar and ybar lines, see how much data is in + quadrants, how much in - quadrants.

Strength of correlation says NOTHING about causality!  Strong correlation could be:
     A causes B/   B causes A/  C causes both A and B (lurking C)/  just Chance that they go together in this data set. 

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