Statistics for Data Analyst

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. 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

 3

 4

 1

 2

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

 Determinant of matrix

 Sum of matrix

 Inverse of matrix

 Trace of matrix

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

 $Trace(A+B)=Trace(B+A)$

 $Rank(-AB)=Rank(AB)$

 $Trace(AB)=Trace(BA)$

 $Rank(AB)\ne Rank(BB)$

4. 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\limits_{i=1}^{k}x_i $

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

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

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

 Linear Spane

 None of these options

 Linear Equation

 Linearity

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

 Only one value

 All the values are different

 Same

 Different

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:

 $\sigma$

 $\frac{1}{n}\sigma$

 All of these options

 $\frac{1}{n}$

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

 3

 1

 Infinite

 2

9. 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 $p+2$ degree of freedom

 Chi-Square with $p$ degrees of freedom

 All of these options}

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

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

 $A’A = AA’=I$

 $A’A=I$

 All given Options

 $A^{-1}=A’I$

11. Eigenvalue is often introduced in the context of

 Mathematics

 Linear Algebra

 Inequality

 Geometry

12. 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

 None of these options

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

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

 $\overline{x}$ and $S$ are dependent

13. Eigenvalues and Eigenvectors are only for the matrices

 Digital Matrix

 Identity Matrix

 Square Matrix

 Symmetric Matrix

14. What are Eigenvalues?

 A vector obtained from the coordinates

 A scalar associated with a given linear transformation

 It is the inverse of transform

 A matrix determined from the algebraic equations

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

 Stretched

 Scaled

 Centered

 Pressed

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

 $L_x=\sqrt{X_1- X_2- \cdots- X_k}$

 $L_x=\sqrt{X_1+ X_2+ \cdots+ X_k}$

 $L_x=\sqrt{X_1, X_2, \cdots, X_k}$

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

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

 1

 Positive Definite

 Zero

 Negative Definite

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

 Square matrix

 Triangular matrix

 Identity matrix

 Singular matrix

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

 $a_1X_1 + a_2X_2+\cdots + a_kX_k=1$

 $a_1X_1 + a_2X_2+\cdots + a_kX_k=0$

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

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

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

 Both Eigen values and Characteristic Equation

 Eigenvector

 Characteristic Equation

 Eigenvalues

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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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