Question

In Module 8, we discussed the correlation coefficient of two random variables, say X and Y. Suppose X is the head circumference of a person, and Y is the person's IQ score. If the correlation coefficient is found to be 0.7943, please interpret this with a brief statement. Use your own words!

Answer #1

The correlation coefficient of two random variables, say X and Y. Suppose X is the head circumference of a person, and Y is the person's IQ score. If the correlation coefficient is found to be 0.7943

Interpretation:

1. The correlation is positive, that is the head circumference of a person and his IQ are positively correlated.

If one has the larger head circumference has the higher IQ

2. The value is quite high for the two variables

Higher the value stronger the correlation

X, Y, Z are zero mean correlated random variables with common
correlation coefficient equal to - 1/2 and all variances equal to
one.
a. Find the best linear estimate of Z in terms of X and Y ?
b. Find the best linear estimator for X in terms of Y and Z?
c. What are the minimum mean square estimation errors in the
above cases?

X, Y, Z are 3 independent random variables. We know that Y, Z is
the 0-1 random variables indicating whether tossing a regular coin
gets a head (1 means getting a head and 0 means not). We also know
the following equations,
E(X2Y +XYZ)=7
E(XY 2 + XZ2) = 3
Please calculate the expectation and variance of variable X.

Suppose we have the correlation coefficient for the relationship
between two variables, A and B. Determine whether each of the
following statement is true or false.
(a) The variables A and B are categorical.
(b) The correlation coefficient tells us whether A or B is the
explanatory variable.
(c) If the correlation coefficient is positive, then lower values
of variable A tend to correspond to lower values of variable
B.
(d) If the correlation between A and B is r...

15.1The probability density function of the X
and Y compound random variables is given below.
X
Y
1
2
3
1
234
225
84
2
180
453
161
3
39
192
157
Accordingly, after finding the possibilities for each value, the
expected value, variance and standard deviation; Interpret the
asymmetry measure (a3) when the 3rd moment (µ3 = 0.0005)
according to the arithmetic mean and the kurtosis measure
(a4) when the 4th moment (µ4 = 0.004) according to the
arithmetic...

Using the data given below, calculate the linear correlation
between the two variables x and y.
X
0
3
3
1
4
y
1
7
2
5
5
(a)
.794
(b)
.878
(c)
.497
(d) .543
Refer to question 4. Assume you are using a 0.05 level of
significance; is there a
significant
relationship between the two variables x and y?
Yes
(b) no
The heights (in inches) and pulse rates (in beats per minutes)
for a sample of 40...

Suppose we have the following paired observations of variables
X and Y:
X Y
18 40
14 30
20 20
22 20
19 10
27 0
Calculate the values of the sample
covariance and sample correlation between X and Y. Using this
information, how would you characterize the relationship between X
and Y?
(12 points)
Suppose X follows a normal distribution with mean µ = 50 and
standard deviation σ = 5.
(10 points)
What is the...

1.Why we recommend to calculate the correlation
coefficient factor before applying the Regression Analysis? if you
found the r as 0.25, what is your next interpret on next
action?
2.You know that adjusted r2 is one the
primary outputs for each Regression
model. Suppose that we developed two different models (x is
Skill and Y is team performance) with
following r2 :
Model 2: What does the adjusted r2 =
0.78 mean? Explain.
Model 3: What does the adjusted r2 =
0.97 mean? Explain.
Which of these two models do you...

Suppose an investor can invest in two stocks, whose returns are
random variables X and Y, respectively. Both are assumed to have
the same mean returns E(X) = E(Y) = μ; and they both have the same
variance Var(X) = Var(Y) = σ2. The correlation between X and Y is
some valueρ.
The investor is considering two invesment portfolios: (1)
Purchase 5 shares of the first stock (each with return X ) and 1 of
the second (each with return...

Suppose that you have two discrete random variables X and Y with
the following joint probability distribution, which is similar to
the example in class. Fill in the marginal probabilities below.
Possible Values of X
Possible
Values
of Y
1
2
3
4
1
0
18
18
14
2
18
14
18
0
Please input the exact answer in either decimal or fraction
form.

4) The correlation coefficient r is a sample statistic. What
does it tell us about the value of the population correlation
coefficient ρ (Greek letter rho)? You do not know how to build the
formal structure of hypothesis tests of ρ yet. However, there is a
quick way to determine if the sample evidence based on ρ is strong
enough to conclude that there is some population correlation
between the variables. In other words, we can use the value of...

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