MATH 251, P&S I, Fall 2007, Wed. Sept. 12, Day 9 .correction .hit reload

Day 9: Read Normal quantile plots, 80--84+ Normal quantile plot Handout ; then Ch. 2, 2.1(scatterplots) then 2.2 (Correlation)
  next Regression, 2.2  and 2.3.  Memorize formula for r (p. 124) and for slope b (p. 137)
SPSS scatterplot Handout : Handout:  Scatterplots pp.1-3, and  Regression, p.4
Correlation p. 4 top. Linear Regression, rest of p. 4.
 
Hand in: 
Normal quantiles:  Normal quantile plot Handout
p. 92ff.
1.121 (distances: granularity)
1.122  (match the quantile plots)
Use SPSS to make histograms or stemplots, Q-Q plots, and Method 2 Normal quantile plots (like IPS's) for the following.  Comment on what you see.
1.125 (logging) To use each group of data separately, Data>Select Cases (SPSS handout p.5 bottom)     
 1.127 To create the data, put a number in the 100th row of a data file (so SPSS will create 100 numbers in your new variable.)  Transform>Compute: RV.Uniform(0,1) (SPSS handout p. 8 bottom)
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Scatterplots (ch2.1) p. 112ff, mostly
Continue to watch for data variables with the wrong Measure in SPSS.
Using SPSS:  Handout:  Scatterplots pp.1-3,   
2.6 Muslim literacy (note, table 1.2) But use the data file given for ex2.6, because the file at ta1.2 in not in a form that allows an SPSS scatterplot!
2.14 speed/fuel  Also Insert>FitLine>Smoother for this set.
2.13 body mass M//F (use sex as the Legend Variable) 
2.16 icicles
2.18 nematodes   Use Dot-line (Scatterplot handout p.2 top) to get means line.  Sometimes by hand it's convenient to use medians instead of means; easy to estimate in the picture.  BY HAND, Mark the medians for each nematode level and connect with a dotted line.  How different are the two lines?

On a separarate sheet:  Begin the Governors' Salaries HW (p.3, Scatterplot handout.)  You can do 1-5 now.  KEEP till all questions have been answered.
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Correlation 2.2 p. 127ff. Use SPSS for all (top of Scatterplot  handout  p. 4 Regression, p.4 )
2.29 dates' heights.   
2.32 speed/fuel again. 
and 2.40 a,b (Transform/compute will make your new variables.  SPSS Intro handout, p. 8). 
2.33 brand and mileage--outlier
2.28 bio vs. physics  Do 2.10 also.  To get the separate correlations for the 2 icicle groups, you need to select each subgroup (See Scatterplot handout p. 4 top, SPSS intro p. 5 bottom)

Governors' Salaries HW sheet:  add #6 to 1 thru 5, keep it.
 Read, discuss 
p. 112, 2.1, 2.2 
 
  Normal quantiles: 
p. 90, 1.119, 1.120
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Correlation 2.2 , p. 127ff
2.22 a  perch. Look at the bottom of the assignment table for the actual r.

 2.31, 2.34,  (Applet on CD or website)  Use mean x and mean y lines to help "see" r.
2.35 (Marriage ages)
2.37 Teach/research
2.38 blunders

Optional 







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2.7 breeding merlins,  Make the scatterplot by hand if you need the practice.







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 More r practice
p. 128 2.23
 
 

 
2.22b .6821.;
Quiz Friday:  Normal distribution and tables.  68-95-99.7% rule, and problems like those on the Normal Probability Practice Handout .  I will give you copies of Table A; if you have a calculator that does this type of problem, you must show all the work (x <-->z, numbers from the paper table needed) to demonstrate that you can do the problem by hand.

Normal Quantile plots: info on  Normal quantile plot Handout last time
Relationships: (Ch 2 Intro and Sec. 2.1)   Handout:  Scatterplots pp.1-3, and  Regression, p.4
   See Day 8 for notes on 2.1.
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Correlation (Sec.2.2)
CD or Website,  http://bcs.whfreeman.com/ips5e,
  Choose "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.

Section 2.2
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.

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

Observe some correlations with applet
Ahead:
Regression line: Section 2.3, Predicts or estimates a y (vertical) value for a given x (horizontal) value: Straight line!
    Formula yhat = a + b x.
         To predict a y-value for a given x-value, plug the x value into the formula and calculate.
                To do it graphically, use the Up-and-Over method (Fig. 2.12, p.134):
                    Find the x, go straight up to the line, then go over to the y-axis; that y-value is the predicted y.

        a is y-intercept. b  is slope (b multiplies x, the horizontal value):  If x increases one unit, yhat increases b units.
    RegressionSlope.xls or in  ClassMaterial\Math251 IPS5e\RegressionDemosExcel

We all get the same line from a batch of data because we use the "least-squares best fit" criterion (pp. 135-6): we'll investigate this more closely later.

**The Regression line is trying to predict the "average y" for a given x (with the added requirement that it is a straight line).
--For a particular (xo, yo) pair in the data, yo is the observed y.  The y-value you get by plugging xo into the regression line formula is the predicted y.  The error = observed y - predicted y.  (Positive if the observed y is above the line) IPSp.135.
--The line is chosen to minimize these vertical errors.  Practice fitting "least squares best fit" lines with applet    http://bcs.whfreeman.com/ips5e.

--Unless the data lies perfectly on a straight line, the line for predicting weight from height -- "regressing weight on height" --(for example) will NOT be the same line as that for predicting height from weight--"regressing height on weight".  (In-class demonstration)(The picture on p.140 is about this. )
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