Nomundari
Q1
Urantulga
Homework4
12. a)
explanatory
variable
response
variable
expectation
legal consultation
Cost <
(is dependant on the
:
As consultation time
so
,
a
,
expected.
Clinear ?
Ex-Distance from
lighting
Re-Time
delay
of
time)
cost also increases
positive correlation is
increases
9)
-
-
thunder
is
dependant onthedistanateley
Exp :
in
hearing thunder
so ,
a
positive
correlation.
⑧ Ex-Distance from the street light
Re-Apparent
Expi
brightness
As distance increases ,
so anegative
,
brightness
correlationthe
①Exteofona ar
Exp
:
correlation
Likely
strong
heavier
because older
people
Guy
preference
depending
the lighter
form would
random
be
no
may
or
scatter.
cars
.
on
likely
a
13
a)
.
Little
or
randomly
8)
points
clear
association. The
scattered without a
no
A downward trend
are
pattern
as 1 variable
meaning
increases the other decreases
a
,
,
,
so
negative
association.
2)
A linear association. Clear
d)
A
association
moderately
strong
but with some scatter.
either
...
straight-line trend ,
positive or negative.
.
I trend is visible
e) A very strong association. Data points are
line
clustered around
tightly
16
a
.
speed of winning horses over time ,
and expect performance to improve over time .
However the increase shown in the scatterplot is not
slow down over time
uniform, performance
gains may
8 10 736)
a
c (0 957)d 70 04
( 0 977)
I
the
see
.
17)
40
.
-
-
-
-
.
.
.
.
a) the scatterplot shows a negative correlation
which
directly relates
rates increase,
back to
mortgage
the
loan
loan as interest
amounts decrease
3)
correlation it a
is
change
Standarzingdent
a)
changing
d)
If the
units does not affect
new
data
correlation
.
point follows the existing trend,
the correlation will remain similar. However the
actual impact depends on whether this new point is an
outlier
.
not
or
el Correlation
a
4)
Q2
does not
relationship but
causation . The data show
imply
do not
they
cause and effect
prove
Just like before Kendall's tal only
and
association , not direct cause
*
26 .
Sx
2
c)
0
0 8
3713
0
1 4
18
.
37 + 15
=
.
.
4
-
=
d)
=
(2)
( 0 3)x4
=
-
.
60
=
0 9
=
40
=
+(8)
.
y
1 2
-
=
=
.
32
-
2x
2x
-
14
=
2x
1
-
=
7
1- 1 2)(25)
.
24 + 30 = 54
54- 1 2x
.
0 940 4667 = 0 42
.
=
.
10 42 + 200)
.
-
44+ 0 42X
32 = 2x
50 = 24
.
i
6) 8,
-
X=
4
.
8
y = 5 + 13x
-
0 77 =
18
13x
( 0 3) +
:
18 = 32
=
=
.
9
.
.
=
.
52 = 13x
=
% = 54-1 2x
8 4
37 = 15 + 13x
a) 31
0 3
10
7
X
y
8
-
bo + Sex
r
24
.
d)
Sy
shows
effect
.
44 + 0
.
42X
.
=
40 84
-
=
-
44
.
4 r
=13 ==
d)Sx
28
·
4
=
-
plot a
2
-
:
(7) =
Sx = 1 4
.
Randomly scattered
Residuals
Thissuggests that alinear modea
pattern in the residuals .
in Residuals
plot f this Curved pattern
that
-
nonlinear
suggests
relationship exists in the data. A
a
linear
model
not
is
.
appropriete
spread.
plot ( Increasing
that the variance is
suggests
not constant
...
44·
a)
From the residual
plot
not appeartobe a
,
there does
pattere
clean
appropriate
model could not be
near
.
R2 is what indicates how much of
8) the
attendance
variation
is
in
explained
6)
by
The residuals
systematic
d)
runs
scored.
do not show
pattern
with
a
clear
a
by
o
attendance is
higher
dodgers
have
than predicted
The
,
meaning they
&positiveresidualindicatinga scored
influencing
are
48
.
a) j
8)
=
attendance .
- 12 882 + 59 389 (Runs)
.
,
x = 750
y
=
-
12 , 882 + 159 389 + 750)
.
y
=
J
=
-
12 , 882 + 44 547 75
,
.
31
,
659
75
.
the estimated
attendance
home
averagewith 750
for a team
is 31 660 fans ·
runs
c) The slope
every
v
is
.
59 389
for
meaning
additional run scored
the
,
.
,
attendance increases
average
59 389 people Which could mean
has a small but positive
runs scored
effect on attendance .
Ey
d)
home
.
.
A
residual in this context
would mean that the actual
attendance is lower than the predicted
negative
.
This
would
mean
that other
factors
influence
attendancebeyon so
Q38) The
scatter
plot shows a
positive relationship
and
height. A
clear
between
linear trend is
shal size
visible.
Fig. 1. Scatterplots of height
-
135
-
y
=
65 97 + 1 72x
.
X
*
125
X
Y
Y
**
10
X
***
X
115
Shoe size
X
.
130
20
vs
Y
I
30323436
28
.
shoe
size
6) The correlation coefficient indicates
lin
detail)astrongpositive correlationMeaningea
.
du
Sy
Sx
=
=
=
870
0 8729
.
6
3
.
.
1820
60
X
=
31 73
.
Y
.
=
increases
shoe
Ey
=
7287
1 72x31 73
.
.
66 1244
.
.
.
us
1
size
.
66 12 + 1 72X
tells
d) The equation
of
unit
increase
-
.
120 7 am
3
.
60 = 120 7
=
.
8, = 1 72
1287
-
6 1820
8729 +
.
in
1 72cm
of O would
.
.
for each
shoe
size ,
Theoretically
be 66 12
.
,
Height
a
cm
and
R2
the
=
0
762
.
=
76
2 % of the variation
.
a
height can explainedby she a
Q4a)
Fig
.
y
-
40
be
=
-
2 Tree diameter
.
0 97 + 2 21x
us Age
.
.
X
Y
35
X
X
N
-
0
X
*
25
Y
X
X
X
X
& 20
X
X
15
X
X
10
X
*
x
X
X
X
5X
24681012141618
tree diameter
(inches
6) The scatterplot shows a
relationship
d
Y
=
-
0 97 + 2 21x
.
.
d) Slope (2 21)
strong positive
between tree diameter and
For
-
.
r= 0
.
age
8882
every linch increase in
diameterthe estimated
age increasesa
,
Intercept (-0 97)
.
R2
=
0 789
.
variation
diameter
,
this
means
78 9 %
.
of the
is
explained by
age
a
showing strong predictive relationship
in
tree