Math 151 , Spring 2004, Friday Day 15, March 5After class Hit reload to get most current version

In lieu of class, a few paragraphs: (choose One)
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 "Got Passion", and why I call her a statistician.

E) Nothing.  Counts as a class absence.
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Exams:  Solutions outside my door, on reserve.     Comments
        total #1 #2 #3   #4 #5 #6    #7   #8  10|0
possible100    8 10 19    16 7 19    17    4   9|88
     max100    8 10 19    16 7 19    17    4   9|012244
      Q3 92    8 10 18    16 7 18.75 16    4   8|788
     Med 87.5  8 10 16.5  16 7 17.5  12.5  2   8|0234
      Q1 78.5  8  9 15.25 14 6 17     7.25 1   7|68
     min 69    5  5 12    10 4 13     2    0   7|004
                                               6|9

HW assignment Day 15
Reading:  Finish 2.3, read 2.4.   Skip 2.5. Ahead in Ch. 3.

Hand in LATER:  Nothing to hand in Monday.  Happy weekend! With four facts, from Day 14: See details there.    C.  govsal on avgpay    2.33, 2.30,    2.35--Note Text &Excel files are put in order, so look different,+ Text is MISSING the 23rd point, (5,56).  You can just type it in.   2.47, 2.51    E. RSquared   = = = = = = = = = = = = = = = = = =  A.  Use ResidualsRSquared from the website or the lab to graph these data sets, along with a graph of the residuals.  Print the results, and describe the shape of the residuals (it may help to connect the dots with pencil, to see the pattern.)  a)  x 1 2 8 4 6 9      y 1 3 6 6 7 5  b) x 1 2 7 4 6 9    y 7 6 2 4 2 1 Moore p. 122, 2.36 speed&gas again a, b, c, d.   There is a data file for problem 2.36, and its third column is the residuals (check them against the book). B. Use Author's website, http://www.whfreeman.com/scc, ...Correlation/regression.   Make a cloud of data (about 15 points), put in the regression line.  Play with an outlier: drag a point to the far left (right) and drag it up and down.  Try it if it's in the middle range of x's.  Write answer: Where is it most influential? Now add a bunch more points (50 is max.)  Play with an outlier  again.  Does the outlier have more or less influence with a larger data set? Moore p. 123, 2.38 Gesell first word-point in middle of x range. Get the data into SPSS, delete child 19, graph and get the regression line and r2.  Use the formula on p.117 and graph the line for the full data set by hand on your printout.   r2  for the full data set is on p. 122.  Moore p. 122, 2.37 Calories (You saved these, I think--or, from Moore's files, in  TA02-04) Graph and get lines in SPSS with and without the outliers.  Graph the line for "without outliers" by hand on the printout for "with outliers" so you can compare them better.  Print one more graph (with outliers) and keep it for problem C below.

Read,

Optional          ==== = = = = = =  SPSS will make residuals:  Do Analyze>Regression>Linear (a new menu for us)  Click your variables into Independent (X) and Dependent(Y).  Hit the Button "Save...": Checkbox Residuals: Unstandardized. Continue, Ok out of the menus.  You'll get output; ignore it.  You'll get a new variable, the residuals.  Try it with the data file for problem 2.36, with speed and gas.  You'll get a fourth variable that should be the same as the residuals variable.

Regression-- Review comments
ANY Straight line y = a + bx  (or bx + a):  b, the coefficient of x, is the slope of the line.  If x changes one unit, y changes b units, so b is the rate of change of y with respect to x.  (If y is weight in pounds, and x is height in inches, b is the number of pounds  we expect to see weight go up by, per inch that height goes up by.

"Regression line of weight on height":  height = horizontal (x) axis, weight = vertical (y) axis.
We finished Fact 1; have the rest to go.
Four Facts:  Day 14

LEAST SQUARES PROPERTY
"Residual at x" = y - yhat  = distance between observed y and  predicted y (what's left over after predicting)
    ( Positive if observed is bigger than predicted, negative if observed is smaller than predicted)
Least squares principle:  Find the line that minimizes the sums of the squared residuals.(Here, or in Mac 101, ClassMaterials\Math151\ RegressionDemos\RegressionLine.xls, Squares tab)
       This method of finding a "best fit" straight line for predicting y's from x's was derived mathematically to work well with "joint normal" data--elliptical clouds.  For data of this sort, the line does  give the mean of the y's for each given x (at least in the abstract.)

Drawback if the data is not the "elliptical cloud" type:
     Outliers get their residual distance squared:  May be very influential  in determining where line sits.
             Especially if at lowest or highest x-values, may change slope of line a lot.
              Author's website,http://www.whfreeman.com/scc, ...Correlation/regression.   Play with an outlier.
 (Outliers toward the middle x's may not change the slope, but may affect r and r².)

Plotting residuals:  This amounts to making the regression line into a new x-axis--If you plot the residuals themselves vs. the original x values, without the distraction of the slanted line, outliers and patterns other than the linear (if any) can emerge.
(Here or ClassMaterials\Math151\RegressionDemos\ResidualsRSquared.xls , Graph of Residuals tab.(doesn't have tiny unlined graph)
SPSS can make a new variable of residuals, which you then can use to make a scatterplot. Optional HW.