ST370 Feb 04, 1998

by Thursall Winters and Tracy Lewis

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Summary for 2/4/98

Thursall Winters
Tracy Lewis

Handouts-
  1. solutions to old quiz 1(done for homework)
  2. new homework attached  ( and one problem from book)
       due Wed. Feb 11

Lecture today covers Chapter 11 in cartoon guide
Half of lecture is review for test

Review-

Given ten numbers, be able to find these:
 - Mean
 - Median
 - Sample standard deviation
     (make sure calculator divides by (n-1) not just n)
 - IQR
 - Boxplot (books method)

    * when entering in numbers in calculator- if the numbers are all
very small(.000000000003,etc), it might be better for the calculator if
you entered them in as 3,etc ,and then multiply by 10E-12



Blocking



       0 0 0                        0 0 0
  0 ft ___________________________________________far in the distance

           x x x                       x x x


      0 is Dr.Smith
      x is Tiger woods

     The boxplots for these two golfers show much variability
     when there is too much variability you can try to control this
     by using blocking.



Chapter 11  (cartoon guide)

Regression-

         - Find a line that best fits a set of data points

         - The difference between a point and the line is called the
residual


Fomulas to compute intercept and slope of least squares
  (See pade 199 in Cartoon Guide for an example)

         -Graph of x and y

         -Slop runs directly through point(meanX, meanY)

SSE  sum of squares error
   = sum(yi - Y)           -- Y is mean y
                           -- X is mean x

SSxx = sum(xi - X)^2

SSyy = sum(yi - Y)^2

SSxy = sum((xi-X)(yi-Y))

y = bx + a                -- a is y-intercept, b is slope

b = SSxy/ SSxx      - approximately
a = Y - bX



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Small spread-  all points lie in middle, none near zero or high numbers
Large spread-  points are spread out ranging from low to high, not
    bunched together
Good fit-   values are near line - could be small spread or large
Bad fit-   values are far away from line,  could be small spread or
    large



ANOVA table

Source of Variablity     Sum of Squares
 Regression               SSR = sum(yi-Y)^2
 Error                    SSE = sum(y-Y)^2

 Total(SSR+SSE)           SSyy/(n-1) = sum(yi-Y)^2/(n-1)

 Graph pg 195

    If all points are on the line then  SSE = 0 - made no error.
    If SSR = 0 then all error