Question

3.        

The general manager of a Totalisator Agency Board (TAB) wants to investigate whether there is a relationship between the number of people who attend a race meeting and the amount of money that people place on bets at the TAB. This information is recorded for 10 race meeting as below:          Attendance (‘000)                                         Amount invested ($’000)                      15                                                                       250                      12                                                                       146                      20                                                                       375                      16                                                                       200                      25                                                                       280                        9                                                                       125                      18                                                                       310                      21                                                                       350                      14                                                                       190                          20                                                                       304 Calculate the value of the correlation coefficient, r.

1. Find the correlation coefficient between Snatch record and weight limit.     (0.985)
2. Find the correlation coefficient between Clean and jerk record and weight limit.

                                                                                                                                   (0.970)

3. Find the correlation coefficient between Clean and jerk record and Snatch record.

                                                                                                                                    (0.995)

Answer 1

X	Y	XY	X²	Y²
15	250	3750	225	62500
12	146	1752	144	21316
20	375	7500	400	140625
16	200	3200	256	40000
25	280	7000	625	78400
9	125	1125	81	15625
18	310	5580	324	96100
21	350	7350	441	122500
14	190	2660	196	36100
20	304	6080	400	92416
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
170	2530	45997	3092	705582

SSxx = Ʃx² - (Ʃx)²/n = 3092 - (170)²/10 = 202

SSyy = Ʃy² - (Ʃy)²/n = 705582 - (2530)²/10 = 65492

SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 45997 - (170)(2530)/10 = 2987

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 2987/√(202*65492) = 0.821