1. CORRELATION & LINEAR REGRESSION
C.Adithan
Department of Pharmacology
JIPMER
Pondicherry

2. 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

3. Perfect negative correlation r = - 1.00 Perfect Positive correlation

4. A

6. 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.
Perfect correlation.
Perfect negative or inverse correlation.

7. 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.

8. “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

9. r = 0.85

10. 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.

11. Y
Y = a + bX
b = n/m n a m X

12. Question to be asked before doing linear analysis: Can 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?

13. Thank you