co relation and regression

1. DEPARTMENT OF BOTANY
TOPIC- CORRELATION AND REGRESSION ANALYSIS
BY- SAMEER VAISH
SUBMITTED TO-POORNIMA VAJPAYEE
COURSE- MSC{ENVIRONMENTAL SCIENCE}
SEMESTER-3RD SEMESTER
UNIVERSITY OF LUCKNOW

2. Correlation
Finding the relationship between two
quantitative variables without being able to
infer causal relationships
Correlation is a statistical technique used to
determine the degree to which two
variables are related.

3. • Rectangular coordinate
• Two quantitative variables
• One variable is called independent (X) and
the second is called dependent (Y)
• Points are not joined
• No frequency table
Scatter diagram
Y
* *
*
X

4. 80
100
120
140
160
180
200
220
60 70 80 90 100 110 120
Wt (kg)
SBP(mmHg)
Scatter diagram of weight and systolic blood pressure

5. Correlation Coefficient
Statistic showing the degree of relation
between two variables

6. Example:
Weight
(Kg)
Age
(years)
serial
No
1271
862
1283
1054
1165
1396
A sample of 6 children was selected, data about their
age in years and weight in kilograms was recorded as
shown in the following table . It is required to find the
correlation between age and weight.

7. Y2X2xy
Weight
(Kg)
(y)
Age
(years)
(x)
Serial
n.
14449841271
643648862
14464961283
10025501054
12136661165
169811171396
∑y2=
742
∑x2=
291
∑xy=
461
∑y=
66
∑x=
41
Total

8. Spearman Rank Correlation Coefficient (rs)
It is a non-parametric measure of correlation.
This procedure makes use of the two sets of
ranks that may be assigned to the sample
values of x and Y.
Spearman Rank correlation coefficient could be
computed in the following cases:
Both variables are quantitative.
Both variables are qualitative ordinal.
One variable is quantitative and the other is
qualitative ordinal.

9. Example
Income
(Y)
level education
(X)
sample
numbers
25Preparatory.A
10Primary.B
8University.C
10secondaryD
15secondaryE
50illiterateF
60University.G
In a study of the relationship between level
education and income the following data was
obtained. Find the relationship between them
and comment.

10. Answer:
di2diRank
Y
Rank
X(Y)(X)
423525PreparatoryA
0.250.55.5610Primary.B
30.25-5.571.58University.C
4-25.53.510secondaryD
0.25-0.543.515secondaryE
2552750illiterateF
0.250.511.560university.G
∑ di2=64

11. Regression Analyses
Regression: technique concerned with predicting
some variables by knowing others
The process of predicting variable Y using
variable X

12. Regression
Regression is a statistical measure used in
finance, investing and other disciplines that
attempts to determine the strength of the
relationship between one dependent
variable (usually denoted by Y) and a series
of other changing variables (known as
independent variables)
 Uses a variable (x) to predict some outcome
variable (y)
 Tells you how values in y change as a function of
changes in values of x

13. Correlation and Regression
 Correlation describes the strength of a linear
relationship between two variables
 Linear means “straight line”
 Regression tells us how to draw the straight line
described by the correlation

14. Regression Equation
 Regression equation
describes the
regression line
mathematically
– Intercept
– Slope
80
100
120
140
160
180
200
220
60 70 80 90 100 110 120
Wt (kg)
SBP(mmHg)

15. Exercise
A sample of 6 persons was selected the
value of their age ( x variable) and their
weight is demonstrated in the following
table. Find the regression equation and
what is the predicted weight when age is
8.5 years.

16. Weight (y)Age (x)Serial no.
12
8
12
10
11
13
7
6
8
5
6
9
1
2
3
4
5
6

17. Answer
Y2X2xyWeight (y)Age (x)Serial no.
144
64
144
100
121
169
49
36
64
25
36
81
84
48
96
50
66
117
12
8
12
10
11
13
7
6
8
5
6
9
1
2
3
4
5
6
7422914616641Total

18. 11.4
11.6
11.8
12
12.2
12.4
12.6
7 7.5 8 8.5 9
Age (in years)
Weight(inKg)
we create a regression line by plotting two
estimated values for y against their X component,
then extending the line right and left.

19. Multiple Regression
Multiple regression analysis is a
straightforward extension of simple
regression analysis which allows more
than one independent variable.