Statistics for Data Science & Analytics

Multivariate Analysis term includes all statistics for more than two simultaneously analyzed variables. The post contains Multivariate Analysis MCQs. Let us start with the Online Multivariate Analysis MCQs test.

Multiple Choice Questions about Multivariate and Multivariate Analysis

1. How many Eigenvalues does a 2 by 2 matrix have?

 1

 Infinite

 3

 2

2. The set of all linear combination of $X_1, X_2, \cdots, X_k$ is called

 Linear Spane

 Linearity

 None of these options

 Linear Equation

3. A matrix $A_{m\times n}$ is defined to be orthogonal if

 $A’A = AA’=I$

 $A’A=I$

 $A^{-1}=A’I$

 All given Options

4. Let $x$ be distributed as $N_p(\mu, \sigma)$ with $|\sigma | > 0$, then $(x-\mu)’ \sigma^{-1} (x-\mu)$ is distributed as:

 Chi-Square with $p$ degrees of freedom

 Chi-Square with $p+2$ degree of freedom

 Chi-Square with $p-2$ degree of freedom

 All of these options}

5. If $A$ is a square matrix, then $det(A – \lambda)=0$ is known as

 Eigenvalues

 Characteristic Equation

 Eigenvector

 Both Eigen values and Characteristic Equation

6. A square matrix $A$ and its transpose have the Eigenvalues

 Different

 All the values are different

 Only one value

 Same

7. Let $x_1, x_2, \cdots, x_n$ be a random sample from a joint distribution with mean vector $\mu$ and covariance $\sigma$. Then $\overline{x}$ is an unbiased estimator of $\mu$ and its covariance matrix is:

 All of these options

 $\frac{1}{n}\sigma$

 $\sigma$

 $\frac{1}{n}$

8. Let $x_1, x_2, \cdots, x_n$ be a random sample of size $n$ from a p-variate normal distribution with mean $\mu$ and covariance matrix $\sigma$, then

 $\overline{x}$ and S are not independent

 None of these options

 $\overline{x}$ and $S$ are dependent

 $\overline{x}$ and $S$ are independent

9. Eigenvalues and Eigenvectors are only for the matrices

 Symmetric Matrix

 Identity Matrix

 Digital Matrix

 Square Matrix

10. Length of vector $\underline{X}$ is calculated as

 $L_x=\sqrt{X_1, X_2, \cdots, X_k}$

 $L_x=\sqrt{X_1- X_2- \cdots- X_k}$

 $L_x=\sqrt{X_1^2, X^2_2, \cdots, X_k^2}$

 $L_x=\sqrt{X_1+ X_2+ \cdots+ X_k}$

11. The rank of a matrix $\begin{bmatrix}1 & 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 1 & 2 \\ 1 & 1 & 0 & 0 & 2 \\ 0 & 1 & 1 & 1 & 3\end{bmatrix}$ is

 2

 1

 3

 4

12. Eigenvalue is often introduced in the context of

 Linear Algebra

 Inequality

 Mathematics

 Geometry

13. A set of vectors $X_1, X_2, \cdots, X_n$ are linearly independent if

 $a_1X_1 + a_2X_2+\cdots + a_kX_k=1$

 $a_1X_1 + a_2X_2+\cdots + a_kX_k\ge0$

 $a_1X_1 + a_2X_2+\cdots + a_kX_k\le0$

 $a_1X_1 + a_2X_2+\cdots + a_kX_k=0$

14. If $A$ and $B$ are two $n \times n$ matrices, which of the following is not always true?

 $Rank(-AB)=Rank(AB)$

 $Rank(AB)\ne Rank(BB)$

 $Trace(A+B)=Trace(B+A)$

 $Trace(AB)=Trace(BA)$

15. Let $A$ be a $k\times k$ symmetric matrix and $X$ be a $k\times 1$ vector. Then

 None of these options

 $Trace(A)=$ sum of Eigen Values of $A$

 $Trace(A) = \sum\limits_{i=1}^{k}x_i $

 $Trace(A) = \sum\limits_{i=1}^{k}A_i$

16. A matrix in which the number of rows and columns are equal is called

 Identity matrix

 Square matrix

 Singular matrix

 Triangular matrix

17. The pdf of multivariate normal distribution exists only when $\sigma$ is

 Positive Definite

 1

 Zero

 Negative Definite

18. The eigenvalue is the factor by which the Eigenvector is

 Pressed

 Stretched

 Centered

 Scaled

19. What are Eigenvalues?

 A scalar associated with a given linear transformation

 A vector obtained from the coordinates

 A matrix determined from the algebraic equations

 It is the inverse of transform

20. If $A$ is a square matrix of order ($m \times m$) then the sum of diagonal elements is called

 Sum of matrix

 Trace of matrix

 Determinant of matrix

 Inverse of matrix

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Question 1 of 20

Multivariate Analysis MCQs

• If $A$ and $B$ are two $n \times n$ matrices, which of the following is not always true?
• Let $x_1, x_2, \cdots, x_n$ be a random sample from a joint distribution with mean vector $\mu$ and covariance $\sigma$. Then $\overline{x}$ is an unbiased estimator of $\mu$ and its covariance matrix is:
• Let $x$ be distributed as $N_p(\mu, \sigma)$ with $|\sigma | > 0$, then $(x-\mu)’ \sigma^{-1} (x-\mu)$ is distributed as:
• Let $A$ be a $k\times k$ symmetric matrix and $X$ be a $k\times 1$ vector. Then
• Let $x_1, x_2, \cdots, x_n$ be a random sample of size $n$ from a p-variate normal distribution with mean $\mu$ and covariance matrix $\sigma$, then
• The set of all linear combination of $X_1, X_2, \cdots, X_k$ is called
• A set of vectors $X_1, X_2, \cdots, X_n$ are linearly independent if
• Length of vector $\underline{X}$ is calculated as
• A matrix in which the number of rows and columns are equal is called
• A matrix $A_{m\times n}$ is defined to be orthogonal if
• If $A$ is a square matrix of order ($m \times m$) then the sum of diagonal elements is called
• The rank of a matrix $\begin{bmatrix}1 & 0 & 1 & 0 & 2 \ 0 & 0 & 1 & 1 & 2 \ 1 & 1 & 0 & 0 & 2 \ 0 & 1 & 1 & 1 & 3\end{bmatrix}$ is
• If $A$ is a square matrix, then $det(A – \lambda)=0$ is known as
• The pdf of multivariate normal distribution exists only when $\sigma$ is
• The eigenvalue is the factor by which the Eigenvector is
• Eigenvalue is often introduced in the context of
• How many Eigenvalues does a 2 by 2 matrix have?
• What are Eigenvalues?
• Eigenvalues and Eigenvectors are only for the matrices
• A square matrix $A$ and its transpose have the Eigenvalues

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