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application of statistics in educational research Relationship Correlation And Regression Analysis

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.

  1. Correlation Analysis
  2. 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.

  1. 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 co-efficient 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) x2 y2 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.

  1. Regression on equation y on x is:

y = a + bx

  1. 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
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

 

  1. 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

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