Answer to Question #268717 in Management for Odu

Question

The following sample observations were randomly selected.

X 4 5 3 6 10

Y 4 6 5 7 7

Determine the regression equation. (6 marks)

i. The following hypotheses are given.

1

: 0

: 0

H

H





=



A random sample of 12 paired observations indicated a correlation of 0.32. Can we

conclude that the correlation in the population is equal to zero? Use 0.05 level of

significance. (3 marks

Answer 1

The following sample observations were randomly selected.

 

 

 

X 4 5 3 6 10

 

 

 

Y 4 6 5 7 7

 

 

 

Determine the regression equation. (6 marks)

 

 

 

i. The following hypotheses are given.

 

 

 

 

 

1

 

 

 

: 0

 

 

 

: 0

 

 

 

H

 

 

 

H

 

 

 

r

 

 

 

r

 

 

 

=

 

 

 

¹

 

 

 

 

 

A random sample of 12 paired observations indicated a correlation of 0.32. Can we

 

 

 

conclude that the correlation in the population is equal to zero? Use 0.05 level of

 

 

 

significance. (3 marks

 

Answer:

 Correlation quantifies the strength of the linear relationship between a pair of variables, whereas regression expresses the relationship in the form of an equation. 

A regression equation is used in stats to find out what relationship, if any, exists between sets of data. For example, if you measure a child’s height every year you might find that they grow about 3 inches a year. 

A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).

X

4

5

3

6

10

Y

4

6

5

7

7

X               Y             x2        XY

                  

4                4          16                 16

5                 6          25                30

3                 5          9                   15

6                  7          36                42

10                 7         100              70

(Total)

28                 29       186            173

(Mean)

5.6                5.8         37.2           34.6

Formula:

    b XY X Y k X Xk a Y bX = − • − = − − = − = − = − = −− = Σ ΣΣ Σ Σ ( )/ (

b= 173-(28)(29)/5 divide by 186 - (28)²/5

=173-(812)/5 divide by 186 – (784)/5

=-644 divide by -29.2

=-22.05

a=5.8 – (-22.5)(5.6)=- 730.8

In the case of random sample above:

t = r=   = square root of 12-2 divide 1-(0.32)²

= square root of 10 divide 0.8976

=11.1408 square root

= 3.3379

a=0.05

We conclude the correlation in the population is equal to zero ,because P value is more than zero.