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Prof. Siegel Student Name: Spring 2020 Semester Student Telephone Number: Statistics for Social ​Sciences​ – Section FE Examination 1 (30 points/30 points = 100%) ● Please answer each question on the...

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Prof. Siegel Student Name:
Spring 2020 Semester Student Telephone Number:
Statistics for Social ​Sciences​ – Section FE
Examination 1 (30 points/30 points = 100%)
● Please answer each question on the examination sheets
(by the space provided below each exam problem).
● Additional worksheets follow each examination sheet for
the co
esponding exam problem. Please note the
worksheets is used if you need additional space to answer
questions and/or to show work for the problem.
● Please state formulas and work in order to receive the
maximum credit for a problem.
● Scientific calculators (not cell phone calculators) are
utilized for this examination.
● This particular exam is an open book test. Please submit
your completed exam on or before May 7, 2020. My e-mail
address is ssiegel@touro. Thank you.

1) Is the sign (positive or negative) of the slope for the
egression equation always the same as the sign of the
co
elation coefficient? Please give an alge
aic reason
and a statistical reason for your answer. Include in your
discussion the purpose of the co
elation coefficient and
the slope. [5 points – partial credit]
Student Name:
Additional Worksheet – ​For Problem #1
Student Name:
2) Given the independent variable x and the dependent
variable y. The sample data is as follows: n= 7
sum of the product XY = 8​.​ XXXXXXXXXXsum of X = 1​.​957
sum of each individual of X squared = ​.​ XXXXXXXXXXsum of Y = 30​.​1
a) Find the regression equation to predict the value of Y given
a specified value of X. [10 points – partial credit]
) Is there a strong linear co
elation between X and Y? Please
give a reason for your answer. [1 point]
c) In ordered pairs (X, Y) ​X ​is refe
ed to as the independent
variable and ​Y​ is refe
ed to as the dependent variable. For
egression analysis, state another term for how ​X ​may be
efe
ed to and how ​Y​ may be refe
ed to. [1 point each]


Student Name:
Additional Worksheet -​For Problem #2
Student Name:
A gentle reminder- please show work
3a) Given the sample size n = 7 and the sample mean is 73.1
Calculate the sum of the values for the sample. [1 point]
3b) Given the sample size n= 5, ∑ x = 24 and the
XXXXXXXXXXsample variance = 5.7.
● Calculate the sample standard deviation [1/2 point]
● Calculate the ∑ X^2 (the sum of each individual value of X
squared) [1.5 points- no partial credit]
Student Name:
Additional Worksheet – ​For Problem #3
Student Name:
4) State five properties for the co
elation coefficient. Please
discuss the meaning of each property stated (in your own
words). [1/2 point for each property]
Student Name:
Additional Worksheet -​For Problem #4
Student Name:
5a) Please give an (original) example of a continuous random
variable. [1/2 point]
5b) Please give two (original) examples of a discrete random
variable. [1/2 point each]
5c) Given the following discrete probability distribution
XXXXXXXXXXx XXXXXXXXXXP(X=x)
1 20.9
2 21.3
3 24.1
4 19.4
5

● Calculate P(X =5) [1 point]
● Please state and explain two properties for a discrete
probability distribution [2 points each]
Answered Same Day Jun 19, 2021

Solution

Biswajit answered on Jun 19 2021
136 Votes
1 .yes ,sign of slope is always same as sign of co
elation coefficient.
As slope b = r Sy/Sx ,as standard deviation always positive,so slope sign depends on co
elation coefficient sign.
Alge
aically,slope measures angle & co
elation measures the relation in different coordinates between y & x .so sign should be same.
The purpose of co
elation coefficient is to check strength of co
elation & sign of co
elation whereas slope says for each unit change in independent variable keeping other independent...
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