Question

1.      Students in a form three class got the following scores in a particular term:

Student

CAT

EXAM

A

34

50

B

56

57

C

53

87

D

24

47

E

57

89

F

75

45

G

54

63

H

44

72

I

39

80

a) Determine the regression equations of y on x.                              (10 Marks)

b) A student sat the CAT and score 65 but missed the EXAM. What score was he to get if he had sat the EXAM?                                                            (5 Marks)

Answer 1

Here N=9

Mean x i.e $\bar{x}=\dfrac{\sum X}{n}=\dfrac{436}{9}=48.44$

Mean y i.e $\bar{y}=\dfrac{\sum Y}{n}=\dfrac{590}{9}=65.55$

Regression coefficient of y on xi.e. $b_{yx}=\dfrac{n\sum (XY)-\sum X\sum Y}{n\sum X^2-(\sum X)^2}$

$=\dfrac{9(28769)-(436)(590)}{9(22924)-(436)^2}$

$=\dfrac{1681}{16220}=0.1036$

(a) Regression equation of y on x-

$(y-\bar{y})=b_{yx}(x-\bar{x})$

$(y-65.55)=0.1036(x-48.44)\\\Rightarrow y=0.1036x+70.57$

(b) When cat score i.e. x=65 then y

$y=0.1036(65)+70.57=77.3041$

Hence the score for exam is 77.3041.