Answer to Question #272903 in Statistics and Probability for Madimetja

Question

QUESTION 1

Differentiate between multiple regression analysis and multiple discriminant analysis. QUESTION 2

What is the importance of examining the assumptions of linearity and homoscedacity when conducting regression analysis and what are the potential remedies for violations of each?

QUESTION 3

What is multicollinearity?

QUESTION 4

How does sample size impact statistical power and generalizability?

QUESTION 5

What are the three primary issues a statistical analyst should consider when selecting applications of multiple regression?

QUESTION 6

Briefly describe six-stage model-building process

QUESTION 7

Justify the use of a split-sample approach for validating data in multiple discriminant analysis.

QUESTION 8

What are the assumptions of multiple discriminant analysis?

QUESTION 9

How does a two-group discriminant analysis differ from a three-group analysis? QUESTION 10

Why should you stretch the loadings and centroid data in plotting a discriminant analysis solution?

Answer 1

1

Discriminant analysis is similar to multiple regression analysis in many aspects. The primary distinction between these two methods is that regression analysis uses a continuous dependent variable, whereas discriminant analysis requires a discrete dependent variable.

2

For starters, linear regression requires a linear connection between the independent and dependent variables. Because linear regression is susceptible to outlier effects, it's also crucial to look for them. Finally, linear regression presupposes that the data has little or no multicollinearity.

3

Multicollinearity is a statistical phenomenon in which one predictor variable in a multiple regression model may be linearly predicted with a high degree of accuracy from the others.

4

A greater sample size is required for a higher degree of confidence. Given that there is a difference in the population, power is the likelihood that we will uncover statistically significant evidence of a difference between the groups. A higher sample size is required for increased power.

5

Linearity refers to the connection between X and the mean of Y.

Homoscedasticity: For every value of X, the variance of the residual is the same.

Independent observations: Observations are not reliant on one another.

Normality: Y is normally distributed for any fixed value of X.

6

Requirement gathering and analysis:-

Design

Implementation or coding

Testing

Deployment

Maintenance

1) Requirement Gathering and Analysis:-

During this phase, all the relevant information is collected from the customer to develop a product as per their expectation. Any ambiguities must be resolved in this phase only.

Business analyst and Project Manager set up a meeting with the customer to gather all the information like what the customer wants to build, who will be the end-user, what is the purpose of the product. Before building a product a core understanding or knowledge of the product is very important.

For Example, A customer wants to have an application which involves money transactions. In this case, the requirement has to be clear like what kind of transactions will be done, how it will be done, in which currency it will be done, etc.

Once the requirement gathering is done, an analysis is done to check the feasibility of the development of a product. In case of any ambiguity, a call is set up for further discussion.

Once the requirement is clearly understood, the SRS (Software Requirement Specification) document is created. This document should be thoroughly understood by the developers and also should be reviewed by the customer for future reference.

2) Design:-

In this phase, the requirement gathered in the SRS document is used as an input and software architecture that is used for implementing system development is derived.

3) Implementation or Coding:-

Implementation/Coding starts once the developer gets the Design document. The Software design is translated into source code. All the components of the software are implemented in this phase.

4) Testing:-

Testing starts once the coding is complete and the modules are released for testing. In this phase, the developed software is tested thoroughly and any defects found are assigned to developers to get them fixed.

Retesting, regression testing is done until the point at which the software is as per the customer’s expectation. Testers refer SRS document to make sure that the software is as per the customer’s standard.

5) Deployment:-

Once the product is tested, it is deployed in the production environment or first UAT (User Acceptance testing) is done depending on the customer expectation.

In the case of UAT, a replica of the production environment is created and the customer along with the developers does the testing. If the customer finds the application as expected, then sign off is provided by the customer to go live.

6) Maintenance:-

After the deployment of good product on the production environment, maintenance of the product i.e. if any issue comes up and needs to be fixed or any enhancement is to be done is taken care by the developers.

7

When a multitude of factors must be considered, financial planners employ multiple discriminant analysis to evaluate possible investments. MDA is a type of discriminant analysis that statisticians and other academics frequently utilize.

8

Each group's covariance matrices should be (almost) identical. Multivariate linear functions are thought to be able to distinguish between groups. The number of samples (objects) in the analysis must be larger than the number of variables. Each group should have at least two items.

9

 In many cases, the dependent variable consists of two groups or classifications,

for example, male versus female. In other instances, more than two groups are

involved, such as a three-group classification involving low, medium, and high

classifications. Discriminant analysis is capable of handling either two groups or

multiple groups (three or more). When two classifications are involved, the

technique is referred to as two-group discriminant analysis. When three or more

classifications are identified, the technique is referred to as multiple discriminant

analysis.

10

Frequently, plots are less than satisfactory in illustrating how the groups differ on certain variables of interest to the researcher. In this case stretching the discriminant loadings and centroid data, prior to plotting the discriminant function, aids in detecting and interpreting differences between groups.