CORRELATION

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CORRELATION LINEAR REGRESSION

• C.Adithan
• Department of Pharmacology
• JIPMER
• Pondicherry - 605006

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CORRELATION measures the closeness of 2 variables

• LINEAR REGRESSION
• gives the equation of the straight line that best
  describes it
• enables prediction of one variable from the other

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Perfect negative correlation r - 1.00
Perfect Positive correlation r 1.00
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The correlation coefficient (r) ranges from -1 to
1. Value Interpretation Zero
Two variables do not vary
together at
all. Positive fraction Two variables tend to
increase or
decrease together. Negative fraction One
variable increases as the other
decreases. 1.0
Perfect correlation. -1.0
Perfect negative or inverse correlation.
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• If r is far from zero (i.e., significantly
  different from zero), there are four possible
  explanations
• The X variable helps determine the value of the
  Y variable.
• The Y variable helps determine the value of the X
  variable.
• Another variable influences both X and Y.
• X and Y don't really correlate at all, and you
  just happened to observe such a strong
  correlation by chance. The P value determines how
  often this could occur.

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• t test is used to test the significance of r
  value
• Significance is a function of
• Size of correlation coefficient
• Number of observations

Weak correlation (e.g., 0.454) may be significant
if n is large Strong correlation (e.g., 0.872)
may not be significant if n is small
Good correlation does NOT imply cause-effect
relationship
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r 0.85
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• Linear regression
• Analyze the relationship between
• two variables (X and Y).
• Draw the best straight line through the data.
• Used to create a standard curve
• to find new values of X from Y, or Y from X.

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Y
Y a bX
b n/m
n
a
m
X
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Question to be asked before doing linear
analysisCan the relationship between X and Y
be graphed as a straight line? Is the scatter
of data around the line Gaussian (at least
approximately)? Is the variability the same
everywhere? Do you know the X values
precisely? Are the data points independent?
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Thank you