Question

3. For the following Eigenvalues tables, how many Factors are there? Explain

Eigenvalues of the Correlation Matrix: Total = 13 Average =

1

Eigenvalue Difference Proportion Cumulative

1 3.56707480 0.56943025 0.2744 0.2744

2 2.99764455 1.25956706 0.2306 0.5050

3 1.73807749 0.45085244 0.1337 0.6387

4 1.28722505 0.28198745 0.0990 0.7377

5 1.00523760 0.38662334 0.0773 0.8150

6 0.61861426 0.06718656 0.0476 0.8626

7 0.55142770 0.10443379 0.0424 0.9050

8 0.44699392 0.16625812 0.0344 0.9394

9 0.28073579 0.08002691 0.0216 0.9610

Answer #1

Given the eigenvalues, we decide the number of factors on the basis of variance explained by the eigenvalues. The components that explain the higher proportion of variance are chosen first. The components with larger eigenvalues explain more variation.

Now, to decide how much of the variance we need to be explained, for decriptive purposes 80% of the explained variance is a good number. Hence, looking at the cumulative proportion column in the table, we have 5 significant factors.

Calculate the correlation coefficient, r, for the data
below.
Calculate the correlation coefficient, r, for the data
below.
X= -10 -8 -1 -4 -6 -7 -5 -3 -2 -9
Y= -15 -13 4 -4 -7 -11 -6 -2 1 -13

Leading digit
Count
Actual
Distribution
Expected
Distribution
Cumulative difference
1
38
31.1%
2
17
13.9%
3
25
20.5%
4
9
7.4%
5
9
7.4%
6
3
2.5%
7
11
9.0%
8
5
4.1%
9
5
4.1%
Total
122
100.0%
KS
Cut-off
How to find Expected Distribution and Cumulative Difference
using Excel functions?

Prior Inpatient Length of Stay and Current Inpatient
Length of Stay
1. What is the correlation coefficient (rounded to two decimal
places) between Length of Stay and Current Inpatient Length of
Stay?
2. Is the relationship between Length of Stay and Current
Inpatient Length of Stay positive or negative?
3. Is the relationship between Length of Stay and Current
Inpatient Length of Stay weak, moderate, or strong?
Prior Inpatient Length of Stay
Current Inpatient Length of Stay
3
9
6...

Compute the Pearson correlation for the following set of scores.
(Round to 3 decimal places)
X
Y
2
5
6
2
7
8
5
6
3
6
7
1
r =

Refer to the following matrices.
A =
1
−8
7
−3
−18
6
5
8
6
0
5
8
3
4
8
−2
B =
4
−7
4
0
1
4
9
5
3
−3
0
9
C =
1
0
3
2
8
D =
1
9
−7
0
What is the size of each matrix?
A
____× ____
B
_____× _____
C
____× ____
D
____× _____

As a sociologist, you are interested in better understanding
what factors impact personal annual income. To explore this topic,
you asked participants to report how many years of education they
have attained as well as their salaries. What is the
correlation between education and income in the sample
below?
Case
Education
(X)
Salary (in thousands)
(Y)
1
14
46
2
16
85
3
15
51
4
13
69
5
15
64
6
16
71
7
14
61
8
13
54...

Determine the Pearson product-moment correlation coefficient for
the following data.
x 1 10 9 7 5 3 2
y 8 4 6 5 7 7 8
(Do not round the intermediate values. Round your answer to 3
decimal places.)
Correlation coefficient, r =

As a sociologist, you are interested in better understanding
what factors impact personal annual income. To explore this topic,
you asked participants to report their father’s income as well as
their own salaries. What is the correlation between
parent and personal income in the sample below?
Case
Parent Income (in thousands)
(X)
Personal Income
(in thousands)
(Y)
1
39
68
2
62
82
3
44
72
4
44
65
5
43
77
6
75
98
7
69
65
8
62...

Determine the Pearson product-moment correlation coefficient for
the following data.
x 1 11 9 6 4 3 2
y 10 4 5 5 7 7 8
(Do not round the intermediate values. Round your answer to 3
decimal places.)
Correlation coefficient, r =

Problem 3
Given a BST with N nodes, how many tree shapes are there with
height N-1? Explain your reasoning.
Problem 4
Given a BST with N nodes, how many tree shapes are there with
height N-2? Explain your reasoning .
Problem 5
Consider an empty 2-3 tree. Draw the tree after each of the
following operations is executed:
insert 0, insert 9, insert 2, insert 6, insert 7, insert 3,
insert 8, delete 2, delete 6

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