Math 151 , Spring 2005, Day 14 Wed. Mar.1 Hit reload...After class


I will be in my office regularly MWF's till about 4, and most Thursdays 12-12:30, 1:45-2:15.
HW Day14
(Re)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 Ch8, AS8 Regression
Hand in Monday (From D&V unless otherwise noted)
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Correlation: (more)
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: 
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

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Regression Prep  (Review graphing straight lines if needed--Math clinic) Postpone:
A. Open the Excel file RegressionSlope (or in the folder RegressionDemosExcel for D&V in ClassMaterial\Math151 D&V).  Change x-y values in the yellow boxes and watch the line change.  Change x-values in col. F and watch the "run" (red line) change, in the rightmost 2 graphs. Notice the slope = the coefficient of x = the rise/run = increase in y per unit increase in x.  Fix it so the increase in x (the "run") is exactly 1.  Print page 1 to hand in.

B. Practice fitting lines:  Use the Moore website ("Do this" below) and try to fit at least 4 different data sets. Write down on your paper what you discovered (were your judgment errors consistent in any ways--did you have any surprises?) 

 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)

Friday Day 15:
A) Class optional: I will discuss exam, answer questions, review what you would like.  Please email me and let me know what you would like to see.  Meet in Mac 126

In lieu of class, a few paragraphs: (choose One)  (separate from other HW)
B)    A paragraph describing one of the workshops/talks you attended,
  + a paragraph or so on a situation where organized data could be useful to an activist  working for a cause (either data which was cited in a workshop you attended, or a place where you could see that information could help make or strengthen the "case" for a cause, or be useful in improving the activist's skill in some way.)
C)  Find one or more graphs, charts or tables of numbers in the popular press or on the web. Hand in a copy of it/them.  Explain what it's about and what it says, and critique it as to how well it conveys the information.  If you can do it better, redo it.
D)  Research Florence Nightingale, primordial activist and statistician.   Report why/how she fits into this year's theme of "The Activist's Toolkit", and why I call her a statistician.  (A websearch is quickly fruitful.)
E) Nothing.  Counts as a class absence.
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Exams:  Solutions outside my door, & will go on reserve  Comments
       total #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11  9|113
possible 100  4 12  8 10  8 21  8  9 10  6   4   8|89
      max 94  4 12  8 10  8 21  8  9 10  6   4   8|124
       q3 88  4 11  8 10  8 21  8  9  7  6   2   7|79
      med 80  4 10  6 10  8 19  6  9  6  6   2   7|004
       q1 70  1  8  6 10  8 13  5  8  5  4   1   6|7
      min 50  0  6  4  1  3  3  0  6  5  3   0     50, 55

Generally good, gives good foundation to go forward.  Don't coast--it gets harder!
Come see me!! if you're in the lower reaches.

HW questions?  Corn yield.
Continuing Correlation (D&V Ch.7 pp118ff, AS7-3&4) Handout, "some correlations" Day 11

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.   Check in the "Show Mean X & Mean Y lines" box.  See how much is in each quadrant. Compare with correlation coefficient.

Regression line: D&V Ch 8&9, AS8&9, A model that Predicts or estimates a y (vertical) value for a given x (horizontal) value: Straight line!
    Formula yhat =  b0 + b1 x,   yhat =a + b x,  weight = -70 +3 height.  (inches, pounds)
         To predict a y-value for a given x-value, plug the x value into the formula and calculate. 60 inches-->110 lb
                To do it graphically, use the "Up-and-Over" method .
                    Find the x, go straight up to the line, then go over to the y-axis; that y-value is the predicted y.
Start here Monday:
        b0 or a or -70 is y-intercept.
        b1 or b  or 3 is slope (b1 multiplies x, the horizontal value):
                 If x increases one unit, yhat increases b1 units.
                      For every inch of height, the model predicts 3 pounds increase in weight.
    RegressionSlope.xls   (or in the folder RegressionDemosExcel for D&V in ClassMaterial\Math151 D&V)

We all get the same line from a batch of data because we use the "least-squares best fit" criterion  we'll investigate this more closely later.
&& We are trying to find an "average" (mean) y value for each x value, with the constraint that they all lie on a straight line.

Do this: Practice fitting "least squares best fit" lines:  Moore's website,  http://www.whfreeman.com/scc,  (ClickNetscape toolbars to minimize them, if needed.  If line drawing doesn't work, try the newer version at http://bcs.whfreeman.com/bps3e/  )
  Choose "Statistical Applets",  Correlation/Regression Demo.  Check in the "Show least-squares line" box and put in some data points.   Check in the "Show Mean X &Mean Y lines" box; note that line always goes thru their crossing.  Repeat for a few data sets.
--Try fitting the line yourself:  (Uncheck the "Show ..." boxes.) Put in some data points.  Now click Draw Line.  Click and drag in the picture and you'll get a line with 3 blobs. Drag the center and it will go up and down, Drag an end and the slope will change. Put the line in the best place for predicting y's from x's.  If you do well by the "least squares" criterion, the green bar up top will shrink close to 0 (but  you have to be really good.  Dumb.)   Check in the "Show Mean X &Mean Y lines" box; adjust your line.  Check in the "Show least-squares line" box and see how you did.
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