Question

Page 10 of 11 Psyc2F23 F/W 19/20 Initials student ID Please answer questions B3, B4 B5 and B6 in booklet ONE. If you require an extra bonus label them IA and 1B and indicate which questions are in which booklet. B6. Your favourite hockey team, the Toronto Maple Leafs have recently fired their head Mike Babcock after losing the last few games. Looking back on the previous 10 games, y have noticed the players on the Leafs have not been finishing their body checks against other teams they have been playing. You hypothesize that when the team is not scoring they are also not finishing their checks. Note: Even if you are not familiar with hockey, you CAN answer this question. Just think of it as two variable (B and G) and answer the questions. #goals (G) BPG G? Rank B Diff score Rank 1 9 1 225 0 0 Diff score squared 2.25 2.25 2.25 9 8 0 1 1.5 -1.5 -1.5 -3 15 0 18 44 76 324 1 6 4 #body checks (B) 15 16 18 22 19 14 25 21 22 17 189 3.541814 2 4 1936 5776 3 9 0.25 0 0 225 256 324 484 361 196 625 441 484 289 3685 0 16 0 25 4 9 7.5 9.5 7.5 5.5 2 9.5 1 5.5 3.5 3.5 55 2.9907 0.5 0 2.5 5 10 1 4 2.5 7 55 3.0185 0 2.25 5 15625 2. 1764 3 4356 3 2601 21 32607 1.663334760.211 125 42 66 51 437 38.7443 1 -1.5 -1 3.5 9 Σ 69 8.1711 12.25 40.5 4.3378 5 137.0687 2.1213 Answer in booklet 1 a) Determine the equation for the least squares regression line predicting #body checks from #goals. (8 marks) Answer in booklet 1 b) Draw the scatter plot of the data. (This does not have to be precise, just a reasonable approximation i.e. DO NOT spend a lot of time!!) (4 marks) Answer in booklet 1 c) d) e) Draw the regression line on your scatter plot. (3 marks) Answer in booklet 1 note: for 3 marks you must show some work indicating how you choose where to put the line If your team scored 6 goals (G) what would be your prediction for the #body checks (B)? (1 mark) Answer in booklet 1 Calculate the appropriate correlation coefficient for the data. (8 marks) Answer in booklet 1 Explain this correlation in plain English (i.e. how would you explain it to someone who knew nothing about statistics)? (2 marks) What distance above and below the regression line would capture 68% of the data points in the population? (hint, you will need the St error of the estimate) (4 marks) Answer in booklet 1 f) g)

Answer 1

Solution (86) NOTE: Let X= Goals (67) and Y- body cheeks. Given EX= 21 EY: 189. XY-431. - 08 Ey? 3685 n = 10. In generally repression equation Bot B ₂ X ; Û = predicted varable (dependent) Bo - mlúupt B4 = slope X endipendentaralde equallen for P, 8Sxy - SSXX equations for po for po = 9 - Bx. ca) in Slope : B4 8Sxy 8SXX where 88 xy Exy Elx) Ely) - [5 434 - Fo (21)(289) = 437 - 39669

SSxy 40.1 where 85xx = Eye- - [ h 1, 6587 [to (213 69 = 69 -44.1 8SXX 21.9. So then slope, By Sxy SSXX 40.1 24.9 - 1.610442 Pu. ^ 1.6104 .: to find mlévept , Bo T = [X 21 n 10 X = 2.1 1 = 27 볶 n 189 10 V = 18.9 .: intucept Be = V - Best

By = 18.9 -(1.6104)(2.1) 18.9 3.38184 15.51816. M 15.52 - ther regresno egualin for body check from geb/s. respresented as given below. body checked 15.52 + 1.6104 goals. (b) Scalte plot. YA 0 24 23+ 22- 0 211 0 20+ 0 0 Body checke (8) ► K 16 0 15 p 14 0 13 + se 0 El Grecibe 3 4 UT

(C) NOTE: We calculateel Regression.equation vedycheck 1552 + 1.6104 goals. from this equation we man calculate expected mean orauerage ualue for y body check ) af X-o (goals) Geals = 0, body checked So lhus there is the intávcepling point x=0.af y. and the all t-ualues (gatals ualues) U$|| 10 15.52. Bu J. 6104 make 1.6104 Slepe custh segresscon lvien so thu. regressun line en plot ZAT 24 23 22 ( 21 0 20 checked Bodycheck = 15.52 +106104 goals Error of "predicion Juan 0 o hipoq 17 0 16 15 14 0 137 1 AX 2 3 Goals Gel 4 5

E Gruen goals = 6. body checked 15.52 + 1.6104 goals 15.62 + (106104)(6) 15.52 + 9.6624 25-1824. - 25.18. predueked value of body checked at @goals is 25.18. ce) correlation co- -efficient, le y. ? Giuen EX = 21, 3x²= 69 Sxy= 437 Sy=189 Ey?= 3685 :: Y= 8Sxy SSxx Slipy SSxy = 40.1 88 xx 24.9 where 8Syy= Ey?- [+(5:47] 365 - [to (1899] 드 3685-3672.1 Seyy 119.9.

7 8Sxy SSxx SSyy 40.4 (4.9) (419.9) 40.1 V2811.22 < 40.1 53. 0209 0.7563055 yn 0.756 .: correlation coefficient is 0.756.