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

 Both Eigen values and Characteristic Equation

 Characteristic Equation

 Eigenvector

 Eigenvalues

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

 Square matrix

 Singular matrix

 Triangular matrix

 Identity matrix

3. 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:

 $\frac{1}{n}$

 $\sigma$

 All of these options

 $\frac{1}{n}\sigma$

4. 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 dependent

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

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

 None of these options

5. What are Eigenvalues?

 A scalar associated with a given linear transformation

 It is the inverse of transform

 A vector obtained from the coordinates

 A matrix determined from the algebraic equations

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

 All the values are different

 Only one value

 Different

 Same

7. Eigenvalues and Eigenvectors are only for the matrices

 Symmetric Matrix

 Square Matrix

 Identity Matrix

 Digital Matrix

8. 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

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

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

 $a_1X_1 + a_2X_2+\cdots + a_kX_k=1$

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

 $a_1X_1 + a_2X_2+\cdots + a_kX_k=0$

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

 Pressed

 Centered

 Scaled

 Stretched

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

 Zero

 Negative Definite

 1

 Positive Definite

12. Eigenvalue is often introduced in the context of

 Inequality

 Linear Algebra

 Geometry

 Mathematics

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

 3

 2

 1

 Infinite

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

 $Trace(A+B)=Trace(B+A)$

 $Trace(AB)=Trace(BA)$

 $Rank(AB)\ne Rank(BB)$

 $Rank(-AB)=Rank(AB)$

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

 $L_x=\sqrt{X_1, X_2, \cdots, X_k}$

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

 $L_x=\sqrt{X_1- X_2- \cdots- X_k}$

 $L_x=\sqrt{X_1+ X_2+ \cdots+ X_k}$

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

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

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

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

 None of these options

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

 Linearity

 None of these options

 Linear Spane

 Linear Equation

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

 Determinant of matrix

 Trace of matrix

 Sum of matrix

 Inverse of matrix

19. 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

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

 All of these options}

20. 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

 4

 3

 1

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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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