2. SIMPLE LINEAR CORRELATION
DEFINITION OF CORRELATION
• Correlation is a statistical measure that
describes the extent to which two variables
change together. In simpler terms, it helps us
understand whether there is a connection
between two things and how strong that
connection is.
3. TYPES OF CORRELATION
• The following are different types of
correlation:
• Positive
• Negative
• Zero
4. Positive, Negative and Zero
Correlation
• The correlation between two variables is said
to be positive or direct if an increase (or a
decrease) in one variable corresponds to an
increase (or a decrease) in the other.
• The correlation between two variables is said
to be negative or inverse if an increase (or a
decrease) corresponds to a decrease (or an
increase) in the other.
• No apparent relationship between variables.
5. Examples in Business
• Example 1: Positive correlation - Sales and
Advertising budget.
• Example 2: Negative correlation -
Unemployment rate and Consumer spending.
• Example 3: No correlation - Company size and
Employee satisfaction.
6. Properties of correlation
• Range of Values:
The correlation coefficient r ranges from -1 to 1.
r=1 implies a perfect positive linear relationship.
r=−1 implies a perfect negative linear relationship.
r=0 implies no linear relationship.
• Directionality:
The sign of the correlation coefficient indicates the direction of the
relationship.
r>0 indicates a positive correlation (both variables increase or decrease
together).
r<0 indicates a negative correlation (one variable increases while the
other decreases, or vice versa).
• Symmetry:
The correlation between X and Y is the same as the correlation between
Y and X.
8. Scatter Diagram Method
• A scatter diagram of the data helps in having a
visual idea about the nature of association
between two variables. If the points cluster
along a straight line, the association between
two variables is linear. Further, if the points
cluster along a curve, the corresponding
association is non-linear or curvilinear. Finally,
if the points neither cluster along a straight
line nor along a curve, there is absence of any
association between the variables.
12. Karl Pearson’s Coefficient of
Correlation
• The formula for calculating the Pearson
correlation coefficient (r) between two
variables X and Y is given by:
13. Spearman rank correlation
• The formula for calculating the Spearman rank
correlation coefficient ρ between two
variables X and Y with n paired data points (xi,
yi) is as follows:
