Tuitor Marked Exercise 3: Theory Section

Running head: TUITOR MARKED EXERCISE 3: THEORY SECTION
Tuitor Marked Exercise 3: Theory Section
Name of the Student
Name of the University
Course ID

TUITOR MARKED EXERCISE 3: THEORY SECTION1
Table of Contents
Exercise 3: Theory Section..............................................................................................................2
Question 1....................................................................................................................................2
Question 2....................................................................................................................................3
Question 3....................................................................................................................................7
Question 4....................................................................................................................................8
References......................................................................................................................................10

TUITOR MARKED EXERCISE 3: THEORY SECTION2
Exercise 3: Theory Section
Question 1
a)
Slope ( bYX )= Cov ( x , y )
Var ( x )
¿ ∑ ( xi−x ) ( yi− y )
∑ ¿ ¿ ¿
¿ 400
600
¿ 0.67
Intercept ( a )= y−b x
¿ ( ∑ y
n )−b ( ∑ x
n )
¿ ( 2800
20 )−0.67 ( 300
20 )
¿ 140− ( 0.67 ×15 )
¿ 140−10.05
¿ 129.95
b)
Using the slope and y intercept the regression equation to predict y from x can be obtained as

TUITOR MARKED EXERCISE 3: THEORY SECTION3
y=129.95+ 0.67 x
c)
r =Cov ( x , y )
σ x σ y
¿ ∑ ( xi−x ) ( yi− y )
√ ∑ ¿ ¿ ¿ ¿
¿ 400
√ 600 √ 900
¿ 400
24.4949× 30
¿ 400
734.8469
¿ 0.5443
r2= ( 0.5443 ) 2
¿ 0.2963
d)
Testing significance of positive correlation
Hypotheses
Null Hypothesis (H0): The correlation coefficient between two variables is zero that is ρ = 0
Alternative Hypothesis (HA): There is a positive significant correlation between the two
variables that is ρ > 0