Multivariate Statistics

The post is about the MCQs Multivariate Analysis test. It includes a Variance-Covariance matrix, Principal Component Analysis, Factor Analysis, Factor Loading, etc. Let us start with the Online MCQs Multivariate Quiz.

Online Multivariate Quiz

1. Factor analysis pinpoints the clusters of correlations between variables and for each cluster

 High

 Low

 Complex

 Normal

2. In the relation $\Sigma = V^{1/2} \rho ^{1/2} V^{1/2}$, the $V^{1/2} is called

 Covariance matrix

 Standard deviation matrix

 Variance matrix

 Mean matrix

3. In multivariate analysis the distribution of $\overline{X}$ is

 F

 Chi-Square

 T Square

 Normal

4. An advantage of using an experimental multivariate design over separate univariate designs is that using the multivariate analysis – – – – – – -.

 Allows you not to worry about meeting restrictive assumptions characteristic of univariate statistics

 Allows you to look t more complex relationships compared to the univariate analysis

 Provides a more powerful test of your hypotheses

 Both (More complex relationships) and (More powerful test of hypothesis)

5. In principal component analysis (PCA) the first component contains

 Minimum variance

 Mean deviation

 Average variance

 Maximum variance

6. In principal component analysis, the components are

 Uncorrelated

 Correlated

 Deviated

 Collinear

7. A multivariate statistic that allows you to analyze several dependent variables from an experimental design simultaneously is

 ANOVA

 Manova

 Factor Analysis

 Path Analysis

8. In factor analysis the reliable variance

 Total Variance $-$ Error Variance

 Both (Total Variance $-$ Error Variance) and (Common Variance + Specific Variance)

 Total Variance + Error Variance

 Common Variance + Specific Variance

9. Ffactor loading is

 A correlation coefficient between a variable and a factor (cluster of variables)

 The correlation between binomial variable consisting of items which are strongly associated with each other

 Empirically based hypothetical variable consisting of items which are strongly associated with each other

 The correlation of a variable with a whole score

10. In multivariate analysis Var-Cov matrix is

 $\frac{\Sigma (X_i – \mu)^2}{n-1}$

 $\Sigma = E(X-\mu)(X-\mu)’$

 $\frac{\Sigma (X_i – \mu)^2}{n}$

 $\Sigma = Var(X-\mu)’ (X-\mu)$

11. If $X \sim N (\mu, \Sigma)$ then $(X-\mu)’ \Sigma^{-1} (X-\mu)$ is distributed as

 Beta Distribution

 $chi^2$ with $P$ degrees of freedom

 Normally Distribution

 $N_P(\mu, \Sigma)$

12. A multivariate statistic that allows you to investigate the relationship between two sets of variables is

 Discriminant analysis

 Canonical correlation

 Manova

 Multiple regression

13. In PCA, when the variables are measured in different units then PC extracted on the basis of

 Correlation Matrix

 Specific Variance

 Comunalities

 Variance Covariance matrix

14. ——- is used for causal analysis

 Factor analysis

 Path Analysis

 Manova

 Canonical correlation

15. In multivariate analysis, $n(\overline{x} – \mu)’ S^{-1} (\overline{x} – \mu)$ is called

 Multivariate Normal Distribution

 Var-Cov matrix

 Hottleing T Square

 F Distribution

16. In multivariate analysis the distribution of the sample covariance matrix is

 Chi-Square distribution

 Normal distribution

 Wishart distribution

 T-square distribution

17. The goal of multiple regression is to

 Develop causal explanations based on correlational data

 Explained variation in one variable based on variation in a set of others

 Reduce a large number of correlated measures to a smaller number

 Test the effect of set of independent variables on a single dependent variable

18. A factor is a combination of variables

 Multiple

 Linear

 Group

 Complex

19. Correlational multivariate analysis includes

 Multiple regression

 Canonical correlation

 Discriminant analysis

 All of the options

20. A factor loading of 0.80 means, generally speaking, that

 There is no relationship between that variable and the factor

 The item is poorly related to the factor

 The variable is moderately related with the factor

 The item correlates well with the factor, though not perfectly

 Loading …

An application of different statistical methods applied to the economic data used to find empirical relationships between economic data is called Econometrics. In other words, Econometrics is “the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference”.

Online MCQs Multivariate

• In multivariate analysis Var-Cov matrix is
• In the relation $\Sigma = V^{1/2} \rho ^{1/2} V^{1/2}$, the $V^{1/2} is called
• If $X \sim N (\mu, \Sigma)$ then $(X-\mu)’ \Sigma^{-1} (X-\mu)$ is distributed as
• In multivariate analysis, $n(\overline{x} – \mu)’ S^{-1} (\overline{x} – \mu)$ is called
• In multivariate analysis the distribution of $\overline{X}$ is
• In multivariate analysis the distribution of the sample covariance matrix is
• In factor analysis the reliable variance
• In principal component analysis (PCA) the first component contains
• In principal component analysis, the components are
• In PCA, when the variables are measured in different units then PCs extracted on the basis of
• The goal of multiple regression is to
• A multivariate statistic that allows you to investigate the relationship between two sets of variables is
• Correlational multivariate analysis includes
• An advantage of using an experimental multivariate design over separate univariate designs is that using the multivariate analysis – – – – – – -.
• A multivariate statistic that allows you to analyze several dependent variables from an experimental design simultaneously is
• ——- is used for causal analysis
• Factor loading is
• A factor loading of 0.80 means, generally speaking, that
• A factor is a combination of variables
• Factor analysis pinpoints the clusters of correlations between variables and for each cluster

• Partial Least Squares (PLS) Regression is an example of multivariate analysis (MVA).
• Multivariate Multiple Regression is a method of modeling multiple dependent variables, with a single set of predictor variables.
• Testing text and visual elements on a webpage together.
• An example of multivariate data is Vital signs recorded for a newborn baby: This includes multiple variables such as heart rate, respiratory rate, blood pressure, and temperature.

Online MCQs Multivariate

Online MCQs about various Subjects

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.

Please go to Easy Multivariate Analysis MCQs – 1 to view the test

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

R Frequently Asked Questions and Interview Questions