**Professional Assignment 2 – CLO 1, CLO 2, CLO 3, CLO 4, CLO 5**

- The link below directs you to a file that contains mortality information from a nursing home during the year 2015. The variable “died” indicates that if the patient died before the end of the year. Given this data, develop a logistic regression model, which predicts probability of death of a guest during any year by the end of that year, given the age and the dummy variable “gender.”

__https://drive.google.com/file/d/12WjJcBN_4t8N34Tir2-3hy3Aq5u3j_x4/view?usp=sharing__

- The personnel director of a firm has developed two tests to help determine whether potential employees would perform successfully in a particular position. To help estimate the usefulness of the tests, the director gives both tests to 43 employees that currently hold the position. Table 5 gives the scores of each employee on both tests and indicates whether the employee is currently performing successfully or unsuccessfully in the position. If the employee is performing successfully, we set the dummy variable Group is set equal to 1; if the employee is performing unsuccessfully, we set Group equal to 0. Let x1 and x2 denote the scores of a potential employee on tests 1 and 2.

Perform a discriminant analysis on the data and interpret the result, including the confusion matrix. Include all required steps in assessing the final model. By trial and error, find the threshold, which minimizes prediction relative error.

Please provide your work in detail and include in-text citations. At least five references are required for PA’s and CLA’s

**Note:**

**1. Paper needs to be formatted in APA 7th edition**

**2. Explain your work in detail and provide an in-text citation. **

**3. Need to have at least 6 peer-reviewed articles as the references (Recommend to find the articles from ProQuest.**

**4. Need to include the textbook as the references.**

**6. Please find the textbook and class PPTs in the attachment section.**

**7. ** Textbook Information:

Bowerman, B., Drougas, A. M., Duckworth, A. G., Hummel, R. M. Moniger, K. B., & Schur, P. J. (2019). *Business statistics and analytics in practice *(9th ed.). McGraw-Hill

**ISBN **9781260187496

**8. Please find the image of table 5 in the attachment**

**9.** Please find the Course Learning Outcome list of this course in the attachment

Chapter 16

Predictive Analytics II: Logistic Regression, Discriminate Analysis, and Neural Networks

Copyright ©2018 McGraw-Hill Education. All rights reserved.

1

Chapter Outline

16.1 Logistic Regression

16.2 Linear Discriminate Analysis

16.3 Neural Networks

16-2

2

16.1 Logistic Regression

The general logistic regression model relates the probability that an event will occur to k independent variables

The general model is

Y is a dummy variable that equals one if the event has occurred and zero otherwise

Odds ratio is the probability of success divided by the probability of failure

Equation is

LO16-1: Use a logistic model to estimate probabilities and odds ratios.

16-3

LO16-1

Logistic Regression of the Price Reduction Data

Figure 16.1

16-4

LO16-1

Logistic Regression of the Performance Data

Figure 16.3

16-5

16.2 Linear Discriminate Analysis

Classifies an observation and estimates the probability that the observation will fall into a particular class

Calculate the squared distance between each class’s predictor variable value means and an observation’s predictor variable values

Observation put into the class with the smallest squared distance

Easiest classification analytic to use when there are more than two classes

LO16-2: Use linear discriminate analysis to classify observations and estimate probabilities.

16-6

LO16-2

Results of a Linear Discriminate Analysis

Figure 16.11 partial

16-7

16.3 Neural Networks

Regression techniques so far developed for n = 1,000 or less

Not uncommon for data mining projects to have millions of observations

Neural network modeling developed to handle large data sets

Idea is to represent the response variable as a nonlinear function of linear combinations of the predictor variables

Most common is the single-hidden-layer, feedforward neural network

LO16-3: Use neural network modeling to estimate probabilities and predict values of quantitative response variables.

16-8

LO16-3

Single-Hidden-Layer, Feedforward Neural Network

An input layer consisting of predictor variables x1, x2, … xk

A single hidden layer consisting of m hidden nodes

An output layer where we form a linear combination L of the m hidden node functions

16-9

LO16-3

The Single Layer Perceptron

Figure 16.17

16-10

LO16-3

Neural Networks Continued

Because a neural network model employs many parameters, we say it is overparametrized

There is a danger we will overfit the model

Model finds parameter estimates that minimize a penalized least squares criterion

The penalty equals times the sum of the squared value of the parameter estimates

The penalty weight controls the tradeoff between overfitting and underfitting

16-11

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