lecture 11: covariance and correlation - astronomybelz/phys3719/lecture11.pdf · 16 february 2011...
TRANSCRIPT
Lecture 11: Covariance and Correlation
Physics 3719Spring Semester 2011
16 February 2011 Physics 3719, Lecture 11 2
Lab 3 Experiments
● Gravitational Constant G Jensen, Blackmon (AM)● Speed of Light C Ramirez, Thomas (PM)● Electron Charge-to-Mass Ratio e/m Brown, Blatter (PM)● Millikan Oil Drop Experiment Baehr, Martineau (AM)● Photoelectric Effect Peterson, Ingebretsen (PM)● Hydrogen Balmer Spectrum Gibbs, Baird (PM)● Franck-Hertz Experiment Rowley, Bernal (AM)● High-Res Optical Spectroscopy Richards, Topham (AM)
16 February 2011 Physics 3719, Lecture 11 3
16 February 2011 Physics 3719, Lecture 11 4
“Old” Terms
New Term
“Covariance” - form intuitive - tends to vanish if x & y vary independently - reduces to former result if no correlation
16 February 2011 Physics 3719, Lecture 11 5
Zero Covariance
Positive Covariance Negative Covariance
Covariance:
16 February 2011 Physics 3719, Lecture 11 6
Example: Determine the area of a rectangle, with uncertainty, for a series of measurements of its length and width.
16 February 2011 Physics 3719, Lecture 11 7
Example: Determine the area of a rectangle, with uncertainty, for a series of measurements of its length and width.
16 February 2011 Physics 3719, Lecture 11 8
Uncorrelated Errors
● L = 1.96
● W = 1.25
● LW
= 0.14
● (calculated) = 21.3
● (w/o
LW) = 20.8
● (direct) = 20.6
16 February 2011 Physics 3719, Lecture 11 9
Correlated Errors
● L = 1.78
● W = 1.25
● LW
= 1.67
● (calculated) = 25.2
● (w/o
LW) = 19.2
● (direct) = 25.3
16 February 2011 Physics 3719, Lecture 11 10
Correlated Errors
● L = 1.78
● W = 1.25
● LW
= 1.67
● (calculated) = 25.2
● (w/o
LW) = 19.2
● (direct) = 25.3
We need LW
term!
16 February 2011 Physics 3719, Lecture 11 11
Quantifying Correlation in terms of Covariance
● We want to know if two variables (not uncertainties!) are likely to be linearly related.
● e.g. Shoe size and height
● Introduce “coefficient of linear correlation” r:
Shoe Size
Heig
ht
(cm
)
perfect anticorrelation
perfect correlation
16 February 2011 Physics 3719, Lecture 11 12
Look at points from earlier example:
uncorrelated
correlated
16 February 2011 Physics 3719, Lecture 11 13
Significance of r Depends on N
points
16 February 2011 Physics 3719, Lecture 11 14
Example
16 February 2011 Physics 3719, Lecture 11 15
Joke/Rating Correlation Analysis
● Mean x = 25.8● Mean y = 3.98
16 February 2011 Physics 3719, Lecture 11 16
Joke/Rating Correlation Analysis
● Mean x = 25.8● Mean y = 3.98
● x = 9.7857
● y = 0.617738
● xy
= -4.704
16 February 2011 Physics 3719, Lecture 11 17
Joke/Rating Correlation Analysis
● Mean x = 25.8● Mean y = 3.98
● x = 9.7857
● y = 0.617738
● xy
= -4.704
● R = -0.778164
● Pchance
~ 15%