Math 151 , Fall 2005, Day 14 Mon. Sept. 26 Hit reload...

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HW Day14
Reading   D&V Ch7 Scatterplots, first thru 117 (AS7-1&2), then Correlation, the rest. (AS7-3&4) 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.     Read ahead: Ch8, AS8
Hand in Wednesday (From D&V unless otherwise noted)
Scatterplots: (Copied from Day 12)

SPSS Handout: Repeat the work of page 1, and do problems 1-5 on p. 3.  Keep this work and hand it all in when all problems have been assigned. 

HW in Activstats:  Go to Chapter 7, use the menu button with the House icon.  Scroll thru the problem list to find the ones given.  In each problem involving data, a button will allow you to launch SPSS and open the correct file.  Then save the file for yourself, do the analysis. 
OR: Page of Text of problems, with SPSS links
MRA-81-4 (SPSS) Metabolic Rates, M/F
MRA-83-8 (SPSS) Ed. Spending vs. Teacher Salaries 
MRA-80-2 (SPSS)  Speed vs. Fuel Consumption (describe)
TRE-58-26 (SPSS)  Bear neck/weight  ALSO Make a plot with the M&F bears marked differently.  What if any sex differences do you see here?

MRA-95-13 (SPSS, and pencil) Corn plants.  This is a first introduction to the idea of predicting or estimating a "typical" y for a given x value.  Ch. 8 will do an important special case of that. 
- - - - - - - - - - - - - - - - - 
Correlation (beginning): 
SPSS Handout: Do problem 6, p. 3.  Keep this with the previous work.
p. 130 #11, 12  Match # to scatter.  (Use handout of typical ones, AS7-3 Activity 2)
ActivStats: MRA-89-4 (SPSS) Speed vs. Fuel Consumption (cf. MRA-80-2) r~0, why?
+ + + + + + + + + + +
Correlation: (more)  (Problems from D&V)
p.130, 13 lunchtime (SPSS)
  16 Drug abuse (SPSS)
   26 Oil consumption (SPSS) (this is another timeplot)
   23 Correlation errors
A. 
If women always married men who were 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 4-5 couples with different x's)
Your click-in-the-Circle Data: Created &saved Day 1, ACT 2-2 or 3
ActivStats(Ch.8)HW  ACT-2 Circle Correlations. (SPSS) (copied here) What is the association between the time it took you to click in a circle and the size of the circle?  Does it typically take longer to click in a smaller circle?
What is the association between the time it took you to click in a circle and the distance you had to move to reach the circle?
What is the association between the distance of your click from the center of the circle and the size of the circle?  Can you account for the pattern you see?
Write a paragraph summarizing these relationships.
(If you forgot to make scatterplots before computing correlations, you might want to go back and make them now, before anyone notices.  Be sure to discuss any unusual patterns or points you see in the scatterplot and note how they might have affected the correlations you computed.)
Don't forget to do scatterplots as well as computing correlations. Cf. Circle questions

Read, to 
discuss




-----
+++++

Correl.

p.130, 21Politics,
24Sample
survey
 
Optional 
 
 
 
 

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


If you feel at all shaky about
graphing or using straight lines
(slopes, intercepts) be sure to
do Linear Equations exercise
 and Line Equations, 
Activstats 8-1, activities 3&4
(in preparation for Ch.8)

Relationships:(D&V Ch 7 thru p.117, AS7-1&2  ) Day 12
Handout on SPSS Scatterplots etc. (D&V Ch. 7-10, AS 7,8,9)
govsal_vs_pay.sav  is the file used for most of the handout. (In SPSS for Class 05 folder)



Correlation (D&V Ch.7 pp118ff, AS7-3&4) Handout, "some correlations"

Correlation experiments:
ActivStats 7-3, 2nd activity:  Slider to see shapes ~~ r's.  3rd activity: non-linear data and r's. 4th: center and scale change.
Website,  http://www.whfreeman.com/scc,"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.

The 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.
   "Straight enough."
   Outlier(s)? Do with/without & be cautious.

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

Properties:

  1. Sign of correlation coefficient matches direction of relationship
  2.  Between -1 and +1.   0: no linear relationship,   +1 or  -1: perfect straight line.
  3. Measures relationship--same whichever variable is on the x-axis
  4. "Unitless"--original measurment units are "standardized out"
  5. Not affected by changes of center or scale
  6. Does NOT give info about curved relationships (only measures linear part of relationship).
  7. NOT resistant to outliers--quite sensitive.
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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