Question

The Test results of the Business Statistics were published and the scores were as followed

Students 12 14 10 13 17 12 11 15
Results 5 11 7 8 11 7 6 9

Only 2 decimal places

Determine the α (alpha) Coefficient in the regression equation *

4 points

Your answer

Advise if increasing the number of students to 50 will improve the students’ test scores *

2 points

Remain the same

Increase

Decrease

Determine the β Coefficient in the regression equation *

2 points

Your answer

The association between the students and the results is *

2 points

Positive

Zero

negative

Determine the Correlation Coefficient of the student’s results *

Answer 1

X	Y	XY	X²	Y²
12	5	60	144	25
14	11	154	196	121
10	7	70	100	49
13	8	104	169	64
17	11	187	289	121
12	7	84	144	49
11	6	66	121	36
15	9	135	225	81

Ʃx =	104
Ʃy =	64
Ʃxy =	860
Ʃx² =	1388
Ʃy² =	546
Sample size, n =	8
x̅ = Ʃx/n = 104/8 =	13
y̅ = Ʃy/n = 64/8 =	8
SSxx = Ʃx² - (Ʃx)²/n = 1388 - (104)²/8 =	36
SSyy = Ʃy² - (Ʃy)²/n = 546 - (64)²/8 =	34
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 860 - (104)(64)/8 =	28

α (alpha) Coefficient in the regression equation = y̅ - (SSxy/SSxx)* x̅

= 8 - (28/36)*13 = -2.11

Advise if increasing the number of students to 50 will improve the students’ test scores = Increase

--

β Coefficient in the regression equation = SSxy/SSxx = 28/36 = 0.78

--

The association between the students and the results is = Positive

--

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 28/√(36*34) = 0.80