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WorksheetsEM.lab13.2023
Total questions: 18
Worksheet time: 9mins
Name
Class
Date
1.
What is the formula for calculating the expected value of a discrete random variable?
a)
E(X) = Σ(x * P(x))
b)
E(X) = Σ(x - P(x))
c)
E(X) = Σ(x + P(x))
d)
E(X) = Σ(x / P(x))
2.
E(aX+b)=
a)
a*E(X)+b
b)
E(X)/a + b
c)
a*E(X)
d)
E(X)
3.
Which of the following is a property of covariance?
a)
Cov(X,Y) = E((X - E(X))(Y - E(Y)))
b)
Cov(X,Y) = E(X)E(Y)
c)
Cov(X,Y) = E(X)/E(Y)
d)
Cov(X,Y) = E(X + Y)
4.
What is the formula for calculating the correlation coefficient between two random variables X and Y?
a)
ρ(X,Y) = Cov(X,Y) / (σ(X) * σ(Y))
b)
ρ(X,Y) = Cov(X,Y) * (σ(X) + σ(Y))
c)
ρ(X,Y) = Cov(X,Y) * (σ(X) - σ(Y))
d)
ρ(X,Y) = Cov(X,Y) / (σ(X) + σ(Y))
5.
What does the coefficient of determination measure?
a)
The proportion of the total variation in the dependent variable that is explained by the independent variable
b)
The correlation between two independent variables
c)
The average of the dependent and independent variables
d)
The difference between the dependent and independent variables
6.
What is the range of the correlation coefficient?
a)
Between -1 and 1
b)
Between -∞ and +∞
c)
Between 0 and 1
d)
Between 0 and ∞
7.
What is the covariance between two independent random variables?
a)
Cov(X,Y) = 0
b)
Cov(X,Y) = -1
c)
Cov(X,Y) = E(X)E(Y)
d)
Cov(X,Y) = 1
8.
Var(X+Y) =
a)
Var(X)-Var(Y)
b)
Var(X)+Var(Y)+2Cov(X, Y)
c)
(Var(X)-Var(Y))^2
d)
(Var(X)+Var(Y))^2
9.
Cov(X + Y, Z)=
a)
Cov(2X, Z) + Cov(2Y, Z)
b)
Cov(X, Z) - Cov(Y, Z)
c)
Cov(X, Z) + Cov(Y, Z)
d)
Cov(X, Y) + Cov(X, Z) + Cov(Y, Z)
10.
For any a>0, the correlation coefficient ρ(aX, Y)=
a)
ρ(X, Y)
b)
a*ρ(X, Y)
c)
a^2*ρ(X, Y)
d)
-ρ(X, Y)
11.
For any a<0, the correlation coefficient ρ(aX, Y)=
a)
-ρ(X, Y)
b)
a*ρ(X, Y)
c)
ρ(X, Y)
d)
a^2*ρ(X, Y)
12.
For any b∈R, the correlation coefficient ρ(X+b, Y)=
a)
ρ(X, Y)
b)
ρ(X, Y)+b
c)
b*ρ(X, Y)
d)
ρ(X, Y)+b^2
13.
For any c, b∈R and a>0, d>0, then the correlation coefficient ρ(aX+b, cY+d)=
a)
ρ(X, Y)
b)
a*c*ρ(X, Y)+b*d
c)
a*c*ρ(X, Y)+b+d
d)
a*c*ρ(X, Y)
14.
In simple linear regression models,
Coefficient of Determination R^2 vs. Coefficient of Correlation r
a)
R^2=r^2
b)
R^2=r/2
c)
R^2=2*r
d)
R^2 ≠ r (No relationships)
15.
What does a low (near zero) correlation coefficient always indicate?
a)
no linear relationship between variables
b)
no relationship between variables
c)
non-linear relationship between variables
d)
strong linear relationship between variables
16.
Coefficient of Determination R^2 is used to identify ................
a)
explanatory power of the regression model
b)
strength of the linear relationship
c)
direction of the linear relationship
d)
direction and strength of the linear relationship
17.
Coefficient of Correlation r is used to identify ................
a)
explanatory power of the regression model
b)
strength of the linear relationship
c)
direction of the linear relationship
d)
direction and strength of the linear relationship
18.
R^2=r^2
a)
for all regression models
b)
only for simple linear regression
c)
only for linear regression
d)
None of them
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