Measure of Relationship
In measurement and evaluation process there are different kinds of variables. For researching and studying we can find the relationship of what kind of relationship is there. We can compare the obtained data. we can find what kind of relationship are variable to other variable. By analyzing data we can develop a new concept or we can prove what kind of relation is there. We use the following two methods to find the relationship between two variables.
- Correlation Analysis
- Regression Analysis
5.1 Correlation Analysis
Correlation Analysis refers the closeness of relationship between the variables and correlation coefficient summarizes the degree and direction of correlation. If one variable’s volume increase, the other variable’s volume also increase. It is known as positive correlation. But if one variable’s value increase, the other variables value increase, the other variables value decrease and it is known as negative correlation. If one variables value increase or decrease, there is not any changes in other variables. And it is known as ‘O’ correlation. It is fully positive while counting.
- Methods of calculation Regression
Mark obtained from Janasahayog Higher Secondary School, Itahari class – 9 students in English and Science is given below is taken to calculate.
Table No. 19
To interpret the correlation the following data is necessary to analysis.
|0.00 to 0.20||Negligible|
|0.20 to 0.40||Low|
|0.40 to 0.60||Moderate|
|0.60 to 0.80||Substantial|
|0.80 to 1.00||High|
Table No. 22
Marks obtain Class IX of English
|English (x)||Science (y)||x2||y2||xy|
The above value (0.4666) shows positive correlation between English and Science marks obtain by the student of class IX. It is moderate reliable and significance result of correlation. The result of correlation indicates the positive correlation between English and Science subject.
5.2 Regression Analysis
Regression Analysis is used by Sir Fransis Galtan at first in 1977. It also shows the relation between two variables Galtan has used regression analysis in the study of relation between father and son. It finds the relation between two or more than two variables as average relation. It is used in educational sector and psychological sector to find the relation. The regression analysis is two types. It describes between two variables. It is known as line or regression analysis. But if it describe more than two variables it is known as multiple regression analysis. The regression analysis is a statistical process with the help of regression analysis we can predict known variables value to other unknown variable value. There are two regression line. X dependent variables and y independent variables. Than regression line is x on y. In this way x independent and y dependent variables regression line is y on x.
- Regression on equation y on x is:
y = a + bx
- Regression equation x on y is:
x = a + by
To calculate a and b, the following equation to be made for xy.
Calculation of regression equation on the bases of mark obtained by class XI student of Janasahayog Higher Secondary School, Itahari. (Only 20 student are taken)
Table No. 23
for calculating regression Equation class XI in subject Nepali and English
|Nepali (x)||English (y)||x2||y2||xy|
- Equation of y on x.
y = a + bx
the two equation are
By substituting the value from the table in equation ( i ) and ( ii )
708 = 20 × a + b × 854
20 a + 854b = 708 …………………. ( iii )
or, 34881 = a × 854 + b × 47116
854a + 471166 = 34881
or, 854a + 47116b = 34881 …………….. ( iv)
To find the value of b multiple equation ( iii), with 854 and educational (iv) with 20, than subtract ( iv),
Substitute the value of ‘b’ in equation iv:
854a + 47116 × 0.44 = 34881
or, 854a = 34881 – 20731
or, 854a = 14150
Now, put the value of a
y = a + bx or y =16.57 + 0.44x
In this way Regression equation x on y.
x = xa + by
From the table we put
854 = 20a + b708
or, 20a + 708b = 854………………. ( iii)
or, 708a + b × 29414 = 34881 ……………. (iv)
708b + 20a = 854…………………… (iii)
Or, 29414b + 708a = 34881………………(iv)
Multiply equation iii with 708 and (iv) with 20 then subtract
By putting the value of a and b on x = a + by then the equation becomes as following:
The Regression equation of x on y:
x = 4.81 + 1.07y………………… (i)
The regression equation of y on x.
y = 16.57 + 0.44x………………(ii) Let, x = 10
|Equation x on y
x = 4.81 + 10 × 1.07 = 16
= 4.81 + 20 × 1.07 = 26
= 4.81 + 30 × 1.07 = 37
= 4.81 + 40 × 1.07 = 48
= 4.81 + 50 × 1.07 = 53
The equation y on x.
y = 16.57 + 10 × 0.44 = 21
= 16.57 + 20 × 0.44 = 26
= 16.57 + 30 × 0.44 = 30
= 16.57 + 40 × 0.44 = 34
= 16.57 + 50 × 0.44 = 39
from the above regression equation the conclusion is the value of variables depend one another value the equations shows the variable of equations Y on X is less than X on Y .There is positive relationship between two variable. The regression line interests at point (20, 26) on the axis. Which value depend one other and can find the value of one variable by substituting in the equation and vice versa