ANOVA and Least Square



ANOVA and Least Square

Linear Regression Method

The linear regression method is used to find the relationship among the variables. 1 variable acts as dependent variable while others act as independent variables (Hastie et al, 2009).

Limitations of Linear regression

The relationship between the variables should be linear

Dependent variable acts as random variable while independent variable is a set of multiple values (Seber, G. A., & Lee, A. J, 2012).

Dependent variable possess have equal variances in conditional distributions.

Equation of the Regression Line

X

Y

-7

-12

-2

-8

5

9

1

1

-1

-5

-2

-6

0

-1

2

4

3

7

-3

-8

Table 1

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

-1.102

.606

-1.819

.106

X

1.996

.186

.967

10.731

.000

a. Dependent Variable: Y

Table 2

According to Table 2 the regression will be:

Y= -1.102 + 1.996X

The above calculated regression indicates that by changing one unit of X there will be change of 1.996 units of Y.

In the above table2 the slope) is -1.102 and coefficient of variable X is 1.996 therefore the predicted value of y can be calculated as follow when the value of X=-2

Y= -1.102 + 1.996(-2)

Y= -1.102+-3.992

Y=-5.094

Now the predicted value of Y is as follow when the value of X= 4

Y= -1.102 + 1.996(4)

Y=6.882

Equation of the Regression Line

The regression shows that Score is dependent variable while hour is independent variable. Table 3 shows the data of both the variables.

(Hours)X

Y(Score)

3

75

5

90

2

70

8

98

2

76

4

88

4

95

5

99

6

98

3

81

Table 3

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

66.399

4.882

13.600

.000

Hours

4.905

1.071

.851

4.582

.002

a. Dependent Variable: Scores

Table 4

The estimated equation from the results of above table is

Scores = 66.399+4.905Hours

It means that when there is change of 1 hour of study of exam it will increase the score

up to 4.9 .

According to the results of Table 4 which shows the estimation of regression the final exam scores can be calculated as follow for the students who studied 4 hours or X=4

Scores= 66.399+4.905(4)

Scores = 86.09

Furthermore the final exam scores of those students who studied 6 hours are as follow:

Scores= 66.399+4.905(6)

Scores = 95.82

Correlation Analysis

Correlation analysis is used to find the relationship between independent variables ...