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.
Correlation coefficient  Relationship 
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)  x^{2}  y^{2}  xy 
67  83  4489  6889  5561 
69  56  4761  3136  3864 
42  35  1764  1225  1470 
40  41  1600  1681  1640 
48  54  2304  2916  2592 
42  45  1764  2025  1890 
49  41  2401  1681  2009 
40  58  1600  3364  2320 
32  52  1024  2704  1664 
32  57  1024  3249  1824 
40  43  1600  1849  1720 
24  35  576  1235  840 
36  48  1296  2304  1728 
23  44  529  1936  1012 
32  34  1024  1156  1088 
34  17  1156  289  578 
44  11  1996  121  484 
32  17  1024  289  421 
36  39  1296  1521  1404 
20  32  400  1024  640 
14  32  196  1024  448 
24  23  576  529  552 
34  15  1156  225  510 
32  32  1024  1024  1024 
32  16  1024  256  512 
17  34  289  1156  578 
33  39  1089  1521  1287 
33  7  1089  49  231 
19  37  361  1369  703 
34  32  1156  1024  1088 
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)  x^{2}  y^{2}  xy 
35  21  1225  441  735 
35  21  1225  441  735 
51  35  2601  1225  1785 
45  26  2025  676  1170 
47  35  2209  1225  1645 
45  49  2025  2401  2205 
62  51  3844  2601  3162 
69  35  4761  1225  2415 
62  51  3844  2601  3162 
37  41  1369  1681  1517 
45  20  2025  400  900 
40  13  1600  169  520 
34  62  1156  3844  2108 
62  44  3844  1936  2728 
40  35  1600  1225  1400 
42  37  1764  1369  1544 
62  60  3844  3600  3720 
35  27  1225  729  945 
57  40  3249  1600  2280 
41  5  1681  25  20 
 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
ans= 16.57
Now, put the value of a
and b.
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
the value
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