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					AP Statistics

Chapter 3 and 4 Test Review
Scatterplots
   Display bivariate data: Explanatory
   variable on x axis, response of y axis.
   Describing associations: direction, form,
   strength in context
   Outlier: individual data point that falls
   far outside overall pattern of graph
   Influential Point: data point that
   markedly change LSRL if removed
Least Squares Regression Line
                          Correlation Coefficient
   ŷ = a + bx
                          -1 r  1
                          r tells you two things
                          a) slope: +r = + slope
                                       -r = - slope
   a =  - b             b) dispersion of data
                          around line of best fit.
   Use 2-var stats to
                        The closer to 1 or –1 the less
   get these numbers      variation from LSRL
Interpreting the LSRL
ŷ=a+bx
 The slope of a regression line is usually
   important for interpreting the data.
 The regression equation relating number of
   cavities to dental office visits gives
              ŷ=6.7+.5x

 Interpretation: For each additional trip to the
   dentist (x) the LSRL predicts an increase of
   .5 cavities.
Can you read computer output?
Relating the range of motion and age for 12 patients recovering from knee surgery

Predictor Coef                   Stdev           T-ratio         P-value
Constant 107.58                  11.12           9.67            0.000
Age       -.8710                 .4146           2.10            0.062
N = 12 S = 10.42                           R-Sq: 30.6%       R-Sq(adj): 23.7%



  1. What is the equation of the LSRL?
  2. What is the predicted range of motion for a 25 year old
     patient?
  3. What is the value of the correlation coefficient?
Correlation Tidbits
   Every regression line passes through the
   point (,)
   Correlation ( r ) is a unitless measurement
   r measures the direction & strength only of a
   linear relationship between two variables.
   Like the mean and standard deviation r is
   strongly affected by influential points. It is
   not resistant
Coefficient of Determination r2
   The percent of variation in the response
   variable (y) that is explained by the least
   squares regression of y on x

   Remember to interpret in context:
   68% of the variation in airfare can be
   explained by change in the length of a flight
   (distance).
Residuals
   The difference between an observed value of
   the response variable and the value predicted
   by the regression line

   More Simply: actual – predicted = residual
   if the point is above the line + residual
   if the point is below the line - residual
Modeling Nonlinear Data
   A variable grows exponentially if an (x,log y)
   transformation linearizes the data. y = a(bx)
   If a (log x, log y) transformation is linear,
   then the data is best modeled by a power
   model y = a(xb)

   A residual plot of the transformed data should
   show a random scatter of points.
Make sure you understand
how to answer the free
response question from Quiz
4.1.
 You will probably see another
 question like it tomorrow 
Interpreting Correlation and
Regression
Extrapolation: using a regression line
for prediction outside the domain of
values of the explanatory variable

Lurking variables: a variable that has an
important effect on the relationship
among the two variables, but is not
directly included in the study
Interpreting Association
 1. Association  Causation
    one variable causes changes in a
    second variable

    Ex: a drop in outdoor temperature
    causes an increase in natural gas
    consumption
2. Common response: both variables are
   commonly responding to a third
   lurking variable.

   Ex. Both SAT verbal and SAT math
   scores respond to a students ability
   and level of knowledge.
3. Confounding: The effect on y of the
   explanatory variable is hopelessly mixed up
   with the effects on y of other variables

   Ex: Minority students have lower average
   test scores on college exams than white
   students, but minorities (on average) grew
   up in poorer neighborhoods and attended
   poorer schools than the average white. The
   effect of social and economic differences
   mess up our ability to say race explains test
   scores.
Final Tips for success
   Review past quizzes and worksheets
   Read your textbook looking at the
   examples and definitions again
   Get a good nights sleep
   Take a deep breath and smile.
   YOU ALL RULE!!

				
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posted:8/19/2011
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