CORRELATION AND REGRESSION... BEST FOR BSCIT STUDENTS.. HOPE U ENJOY ;-)

1. Correlation And Regression
Created By :-
Shrayas.s
Wesley.V
Tahir hussain Qureshi

2. CORRELATION
• When we have data on only one variable
we can find arithmetic mean , median ,
mode or variance of the variable.
• By saying that marks scored by students
at s.s.c. and h.s.c. are related is not
sufficient to measure degree of
relationship.

3. CORRELATION
To measure the degree of relationship we
have following measure:
1. Scatter diagram method
2. Co-variance method
3. Karl-pearson’s coefficient of correlation
4. Spearman’s rank correlation coefficient.

4. Scatter Diagram
• A scatter diagram is used for analyzing
relationships between two variables
graphically . One variable is plotted on the
horizontal axis and the other is plotted on the
vertical axis.
• Types of Scatter diagram :
1. Perfect positive correlation
2. Positive correlation
3. Negative correlation
4. Perfect negative correlation

5. Perfect Positive correlation

6. Positive correlation

7. Negative correlation

8. Perfect negative correlation

9. Covariance method
• If(x1,y1),(x2,y2),........(xn,yn) are n observation on
bivariate data then covariance between two variables is
defined as
Using covariance the realtion between x and y is interpreted
as under.if cov(x,y)<0 then there is negative correlation
between x and y. If cov(x,y)=0 then there is no linear
relationship nbetween x and y. If cov(x,y)>0 then there is
positive correlation between x and y.

10. KARL PEARSON’S COEFFICIENT
• If (xi,yi),i=1,2,....n are n pairs of
observations on bivariate data then Karl
Pearson’s coefficient of correlation
between x and y is given by:

11. Spearman’s rank correlation
• If (xi,yi),i=1,2,....n are n observation in
bivariate data and Rx denotes the rank of
X observation and Ry denotes the rank of
Y observations then define d=Rx-Ry.
• Rank correlation coefficient between x and
y is

12. Regression
• Regression gives the
functional relationship
between two variables

13.  Regression means estimate value of one
variable when value of other correlated
variable are known.
 Thus to estimate y, for given x,
y is dependent and x is independent
variable.
 whereas to estimate x for given y,
x is dependent and y is independent
variable.

14. Accordingly we have two regression
equation :
1)Regression equation of y on x
2) Regression equation of x on y

15. Regression equation of y on x
 Here y is dependent variable
and x is independent variable.
And we denote By :-

16. Regression equation of x on y :-
Here y is dependent variable
and x is independent variable.
And we denote By :-