Extensive document with answers to all homework exercises, including calculations and further explanations behind answers linked to reading material.
Conclusions (what knowledge/fact to take from the exercise) written down after every exercise.
Received grade 9.6 (average was 5.6)
2)
10 18 ,
1 , 69 46 , 303 1 Standard deviation s
=
.
1 : =
1
=
1
G
1 10 , 20
, 699 , 99
=
, 304 deviation
+ Standard s
3
7
: =
.
=
1 1
G
d) why are the Variance + SD per definition non-negative ?
I both based on the sum of squared deviations (X-)" +
squares can't be negative ,
so sum of
Squares will always be a positive number +
SD is the square root of the Variance +
always a positive
number
Exercise 3
2
. distribution shapes and normal distributions
a) When a variable is
normally distributed the ,
mean is equal to the median
b) When a variable is distributed positively skewed the,
mean is larger than the median .
d When a variable is distributed negatively skewed the ,
mean is smaller than the median
Mean ,
Median Median +
Mode Mode Mode
Median
A
Mean
(+) 1-
Positive skew Normal distribution Negative Skew
Exercise 3.
3 covariance and correlation
a) covariance :
T)
)(y
+3
4
,
Ei(x - ,738
-
=
0
(xy
=
=
N
b) Correlation :
rxy
2xy =0 ,735 09
=
=
c) Sign it ort of the covariance tells us whether the relationship btw the Variables is positive or negative .
4 When positive scores on 1
1
. are accompanied by negative scores on exam 1
. 3, those devictions
will be negative as well .
When many deviation scores are
negative ,
the covariance is likely to be nega
tive .
Size of covariance is determined by the SD of the Variables , which are influenced by the scale on
which the variables are measured .
Size of the covariance doesn't say anything about the size of
the relationship bth the variables .
, a) Why are both the sigh and the size of the correlation informative ?
· sign tells us whether the relationship btw the variables is positive or negative .
The correlation is a
Standardized measure + bounded btw-1 and Can interpret sign + size
.
1
!
I . large
5
Correlation of small . medium and
3
1
: :
:
0
, 0
Exercise 3
.
4 Variance and covariance of composite scores
as calculate composite score Yi Xi +X; for each subject c) Yk Xk+X
1
.
=
=
:
,
Id :
.
1
) Yij =
G 4 .) Xij =
4 Id :
1 .1 Yki =
7
4 .)
Yk1
=
4
2 ) Vij 5) Yij 2) 9 5) 4
=
Yk1 Yk1
=
7 7
= =
.
3) 6. G 3) 3
5
Yij Vij Yk1 6) Yk1
=
=
7
=
=
b) Calculate the meantvariance of new Variable
Vi Using regular' formulas :
37
* *,
5
=
=
6
, 17
C) ,3
LT G
. 8334 25 , 33
gi
Z
.1395 , 867 4 , 225 . 054
6
4) Both the Variance and the covariance of a composite score can be calculated in 2 ways +traditional
formulas or those for composite scores , which you use depends on available information
· When scores on diff .
Variables given traditional
:
·
when COVGriance Variance matrix given :
composite formula
Exercise Binary
5
3
. :
items
EiX
=1
a) ·*
5
* ,
=
5
=
= ,
Px
=
0
N
0
2
5(1 5)
5
b) , , . 25
-
= =
0 0 0
5
s =
45 =
0
,
189
C k 726
,
=
=> 0
199 + 71
4) 50 ,726+ (1 -
0
, 726)
5 =
0
,
446
,Exercise 3
6
. 12-scores and converted standard scores)
a) Exam course 1
1
.
# ,5-7,
2
, 2302
7
1.
)
5 =
7 , + z-Score :
=
0 et ...
b) Correlation using -scores :
2 zxzy 2
. 6072 = .
434
Txy
=
0
=
N G
c) Convert exam course to a 1-100 scale with SD =
10 and mean I = 50
T =
/Snew) + Knew
0 , 2302 + 10 + 50 52 , 302
=
a) The Maximum possible score on exam 1
3
. is 10 . The z-score associated with a score of
10 is 2 49
. + T-score becomes 2
49 *10 +50 =74 .
. 9 (rounded to 75) .
Therefore ,
given
the Standard deviation and mean calculated on .
3
1,
it's not possible to get a T-score
Of above 75 .
The minimum possible score on exam 1 3
. is 1 +z-score of -4 .41 +T-Score becomes
-
4 4110
. + 50 =
5.
9 (rounded to 6)
.
Thus ,
given the SD + mean from 3
. 1,
it's not possible
to get a T-score below .
6
Percentile F(x)
Exercise 3
.
7
ranks and normalited scores
↑
a) percentile rank for score
3309
2
:
w
5 fx) 54) +100
px(Fx-0 600
. (6 -
,
=
0
=
1 , 294 flx)
N 305
55)
,
(11 -
0 +100 =
,75
2
Px
=
,
309
524)100
,
,
135 -
0 =
7 44
Px4
=
309
6) E =
100 and Sa =
15
Ilook up z-scores corresponding to the percentile ranks . Then , calculate T-scures with
formula T =
z(snew= 180) +
(Enew =
15)
, no m w or DC H4 :
Exercise 4 .1 :
NUMBER OF DIMENSIONS
a) 3 Ways to use the eigenvalues to assess #of dimensions :
1) Examine relative size of eigenvalues and find point at which the difference between values becomes
relatively small
2) Eigenvalue Greater than 1
0
. rule :
all dimensions that have eigenvalue greater than 1
.
8
3) Examine scree plot +
trying to find levelling-off point point of inflection) :
the number of dimension
We commonly consider is 1 less than the point where graph levels off
look for advantages and disadvantages in other notes
Exercise 4 . EIGENVALUES AND EXPLAINED VARIANCE
2
:
9) Calculate eigenvalue for the 6th factor :
·
the sum of all eigenvalues is always equal to the total number of variables (3)
Sum of the Other 7
factors is 7
.
4 1
consequently eigenvaire ,
of 6th factor is 1-7 .4 =
0
,
6
6) Calculate the percentage of Variance explained + cumulative percentage
:
Variance explained
,
& I factors in total :
Total Value for 6 = 2
2
. =
0
, 275 127 5%
of
7
Amount of factors S
# 108
1 X
I
6) which factor explains the most variance :
The first factor explains most of the Variance with 5
27 , % of the total variance of all s items
a) scatterplot :
·
Based on the screeplot we'd choose 2 factors ,
as the point of inflection is
Point of at the 3rd factor .
X inflection
There are 3 factors with eigenvalve greater than so this criterion would
·
1,
lead to 3 factors
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller christinauhlenbruck. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $10.57. You're not tied to anything after your purchase.
