Diagnosis of correlation from observed data.

1. Diagnosis of correlation
from observed data.
Correlation

2. CONTENTS
•Correlation
•Types of
Correlation
•Problem solving

3. Correlation?
?

4. TYPES
• Positive correlation
• Negative correlation
• Zero correlation
• Simple correlation
• Multiple correlation
• Partial correlation

5. Positive correlation?
?

6. Negative correlation?
?

7. Zero correlation?
?

8. Simple correlation?
?

9. METHODS OF
STUDYING
CORRELATION Karls Pearson’s
correlation
coefficient
Scatter Diagram
Method

10. Scatter Diagram Method?

11. x
Karl Pearson’s)
Correlation
coefficient

12. Correlation coefficient of correlation is independent of change
of origin and scale.
Correlation coefficient lies between -1 to +1, Symbolically
Coefficient of correlation is the geometric mean of regression
coefficients.
If X and Y are independent variables then coefficient of
correlation is zero. However, the converse is not true
Properties of
correlation
coefficient

13. Interpretation
of correlation
coefficient
• The correlation of coefficient measures the
degree of relationship between two sets of
variables. The following guidelines are given
which would help in interpreting the value of
r.
• when r = +1, it means there is perfect positive
correlation between the variables
• when r= - 1, it means there is perfect negative
correlation between the variables

14. • when r = 0, it means there is no correlation between
the variables i.e. the variables are uncorrelated.
• the closer the value of r to +1 or -1 , the closer the
relationship between the variables and the closer
the value of r is to 0, the lesser the relationship.
Interpretation
of correlation
coefficient

15. Problem
Example-1:The following data represent the capital employed and profit 7 farms in an
industrial area of a country:
Capitalemployed (in Tk. crores) 10 20 30 40 50 60 70
Profit obtained (in Tk. Crores) 2 4 8 9 10 15 12
i. Make a scatter diagram
ii. Do you think there is anycorrelationbetweenprofits and capital employed?
iii. Find the Karl Pearson’s coefficient of correlationbetweencapitalemployed and profit
iv. Also interpret the result

16. Solution
We know that the coefficient of regression of y on x
is given by

17. x y X2
Y2
xy
10 2 100 4 20
20 4 400 16 80
30 8 900 64 240
40 9 1600 91 360
50 10 2500 100 500
60 15 3600 225 900
70 12 4900 144 840
x=280 y=60  2
x =14000  2
y 644 yx =2940
Calculation
table

19. tahmid30
Tahmid sparker
tahmidrshid
tahmid-rashid-20995b121