Transcript Slide 1

Chapter 10
10-1
Bivariate Data
(x,y) data pairs
Plotted with Scatter plots
x = explanatory variable; y = response
Bivariate Normal Distribution – for a fixed value of x, y values should be
normally distributed, or at least symmetric and mound shaped.
Linear Relationship
Scatter plot can show if there is a linear
relationship between x and y.
Positive correlation – if low x gives low y,
high x gives high y
Slope would be….
Negative correlation – if low x gives high y,
high x gives low y
Slope would be….
Pearson Product-moment
correlation Coefficient = r
AKA sample correlation coefficient
Number that indicates “strength” of the
linear relationship between x and y
-1 ≤ r ≤ 1
r = ±1  perfect linear correlation
r = 0  no linear correlation
If it is a population correlation
coefficient, use the Greek letter ρ (rho)
Bivariate data (x,y)
r
n xy    x   y 
n x    x   n y    y 
2
2
2
2
Tables will be extremely helpful when you have to do
this by hand! You can make lists to calculate the
data values (i.e. with your cauclator) then put the
numbers into the formulas.
Generalizations
r=1
r=0
r = -1
Generalizations
-1 < r < 0
0<r<1
Example
Let x be the average number of employees in
a group health insurance plan, and let y be
the average administrative cost as a
percentage of claims.
A) Make a scatter diagram and draw the line
you think best fits the data
B) Is the correlation low, moderate or strong?
Positive or negative?
C) Calculate r.
Resources
http://www.evl.uic.edu/cavern/multiperspective/Continuum/Training/sc
atter6.gif
http://www.netmba.com/images/statistics/plot/scatter/scatterplot.gif
http://fmrc.pulmcc.washington.edu/IMAGES/SPEX1.JPG
http://cnx.org/content/m10950/latest/r2.gif
http://www.itl.nist.gov/div898/handbook/eda/section3/gif/scatplo2.gif
http://richardbowles.tripod.com/maths/correlation/scatter3.gif