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Year 11

General Mathematics

BivartateData

Practice Analysis SAC

Reading time: 5 minutes

Writing time: t hour 25 minutes

Student Nanre: Solrho*

Year 11 General Mathematics

The maximum temperature and numbers of ice-creams sold over 12 days at a countrycamival were recorded in the table below.

(a) The dependent variable is lcq,- CtlearyS SrlJ

(b) Display the data on a scatterplot, using gaph paper on the next page.Label each axis with words.

(1 mark)

x-

160 3 l

1 8 0 3 5

150 29

t40 27

t20 25

1 3 0 28

1 1 5 24

1 5 0 32

125 26

1 5 5 a aJ J

10s 22

195 39

Page 2 of8

(4 marks)

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-, -: - 1 ! i : : -az ) : , . : a , / i : 3 , , 2 ll

: - . i . ,l : . l

. . : t - - - tI

Practice Bivariate Data SAC

1".-crearfls so/J

2oo

t7o

l8o

l7o

lbo

l{o

/40

130

t2o

Ito

/o0

7o

8o

/o

6 0

ro

4o

3o

20

I C

-lo

-2o

7"oyr"alr*

Page 3 of8

Year 11 General Mathematics

(c) Estimate by eye the value of the correlation cofficient (r).

r = t o . g(1 mark)

(d) Use the CAS calculator to find the least squares regression line equation. Write allnumbers to two decimal places

(l mark)(e) Write the equation using words for x andy

(1 mark)

(f) Draw this line on your scatterplot (previous page).

(1 mark)

(g) From the equation, predict the number of ice-creams sold when the temperature is 42o.

,t4 = I. z/n to.4 |/fUq = tzTx 42 - /o.+lltvt ! = 2/o.7sl '' ' / a 2 t l

flu" /-o thu ,u*Ln, ,/tLe-crearrts s"/J ^pu// ux="rt4 o L u 2 / t u 1 z m # k s ;

(h) Use your calculator to frnd Pearson's correlation coefficient (,r\, to two decimal places.

r : + O - q 7I

Page 4 of8

(1 mark)

Practice Bivariate Data SAC

(i) Carry out a residual analysis on the data by completing the table below

3 l 3r 27 21 2 { 2g 2+ 32 26 3 3 22 3 ?iCffr1a1q",

sold ;_0IJ.. ' 160 l 8 o tf,) /+o lzo l 3o t l r /f,o t2 r I td t o 7 t7r

t{2-il l7\.oq t+2.+2| 3t .8YI 21.99137.t{| 16.07tdr.25/26.b|t 63. {o 1 o(.93 tK./2

7'ob f ? t 7.r8 , . t z 'l '3t+ '7.ttr- l . 0 1 ' t '23 - 1 . 6 t- 7'f,o - o.f,S -0. t 2

Show at least two calculations foryp."6 and residual

Tht "7nol'o* oLl,;r*l by lle leot(-rquoru' / / r /4 ' / : u n r 7 ) e - - t o ' 4 1rrV

-ntloJ "t,r ceS .efut/o/a,

t I / .eo/outloufiow utt oil = g'z f - * l o t ( l

, A b

/,','ftr*4- r o . Q l

Png"\-r/ cJar/,/,b* Rusar/^r/ =

t

: f z T r 3 t

: t f 2 - 7 4

A L t , :

lr"t :

V r,"/

3f,

d . 2 7 x 3 r - t o . . 4 I

| 7+.0+

A { x = ? l

Ruu;,hJ =R rs;l^J =

/ e o - F z 1 (

7 ' o q

A t x : 3 {

R's;kJ =Prs;"kr,[ =

I eo - t7+ .oq

r.76

Page 5 of8

(7 marks)

I : : -

i . : ' l

I i . : :r li : _ :

- - i ' i '- t -- r '

! - : "j "- -

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: , I - -

a . i. t 7 , - : , : , :3Q , , -

r t :I a I : - " _ g- - - : - J 9 - _ .

j - :

j l - : ' ' . , : .: :r : : -

a - : :. + , - - j - i : '

:

: : : a : ' - - :

. : . . . : : . -I

(4 marks)

Year 11 General Mathematics

fi) PloJ the residual values against temperature.

Res;Jua/

I

7

6

f

tf

3

2

l

o

- l

*2

- 3

-+-r

-b

- 7

- 8

fr'P

(k) Comment on the residual plot.

Page 6 of8

(1 mark)

Practice Bivariate Data SAC

Further investigation was undertaken on synchronised swimmers and a new set of data are shownbelow.

=tL- - 2S ' f *14= 3o

flr" *y= tnslf"=g#: t7z's

ffiriJX I R. - o,,^,7 " .4 /' uffi:ralztr"/o{t t"*

; ; | s . i l {o ' / *nn .| | 1y"4" lln, q ',4/,,nt

ff i-,szrl"""'n H*ofl,L wiil' 41"o rVPh'cs'

0) Display the data on a scatterplot, labeling both axes.

l 6 o

t+o

Page 7 of8

(4 marks)

Year 11 General Mathematics

(m) Graphically (by eye) frt a three-median resression line to the scatterplot in (1). Write thecoordinates of the medians for each group below in the space provided.

X . r= .2 f ,+26 : 2 f , . f , 7L

%p: 27+-31 = 9o ,?-

X r = 3 { t 3 7 - g 4 )L

7* ry= r37.s ) (rr.t, ts:.d)

Ur' *y' 172.r =) ( * , nz.r)

/ " ' r y= te7 . r ) ( r t , / r 7 )(5 marks)

(n) Find the equation of the three-median resression line algebraically. Show all working.

ol n"J 4/," f*J #

t , : / ' u - / " =

(r) n"J il,,a ,7uoho-

c= ! [c i ,*7," / , ) -* ( *

? ) - ( tr't I-z

c = + l ( r v . r+ t 7z . f , - f / ss

C : z o . L f

| 87.r - ts 7.f,

3E - 2(.r= +.72

2 * T m *

4 76

-rile t s o " 4 J

m X + C

Xta - 7L

7/"o eQ(t al'ouwoJJ l'ta,to, /

t = h-/6 x + 2

l t /the 'forrn 4 =t r l

t /o . L r

v

END OF PAPER

Page 8 of8

(3 marks)