WGU C723 Quantitative Analysis for Business

Quantitative Analysis

Analysis using objective data

Qualitative Analysis

Analysis using subjective Data

Response Variable

Another name for the dependent variable

Explanatory Variable

Another name for the dependent variable

Negative Correclation

Correlation that occurs when one variable increases and the other variable decreases

Positive Correlation

Correlation that occurs when one variable and the other

Nonnumeric Data

Data of a form such as words, symbols, or letters that are not used in calculations

Numerical Data

Data represented by numbers

Trendline

Line that shows the general direction of the relationship of points over time

Objective Data

Measurable data often obtained through observations or testing

Correlation

Measure of the strength of the linear relationship between variables

-does not apply cause and affect "shoe size doesn't affect reading ability even though they are closely related in grades school"

-used to compare two variables to determine the strength of the linear relationship between them

Metric

Measurement used to gauge performance

Forecasting

Method or process used to make short range decisions where the actual outcomes have not yet occurred

Subjective Data

Non-measurable data often obtained through surveys or interviews

Descriptive Statistics

The analysis of data, to describe, interpret, and summarize data in a meaningful way

Inferential Statistics

The analysis of data to reach conclusions, generalizations, and estimations based on a small sample of the population

Statistics

The gathering, organizing, and interpreting of numerical data

Moderating Variable

Variable that changes the effect of independent variable on the dependent variable

Dependent Variable

Variable that is being measured or affected

Independent Variable

Variable that is free to change in a given model

Quantitative Analysis: models

-Decision Tree

-Network Diagram

-ANOVA

-Linear regression

-Linear Programming

-Break-even Analysis

-Simulation

-and more

Qualitative Analysis: Models

- Surveys

-Brainstorming Session

-Raking (favorites)

-Subjective Judgment

-and more

PEMDAS

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

* Please excuse my dear aunt sally

Y hat

predictive value

Expressions

consist of numbers, variables and operations

* do not have

Equations and Inequalities

do have

Linear Equation

Type of equation when the slope between any two points is constant

Coefficients are the numbers in front of a variable, while constants stand alone.

Mean

Average

- add all numbers , divide by total of numbers added ie 2+2+2+2=8 8/4=2

Median

Middle

-arrange numbers smallest to largest, which number is in the middle, if even add the two numbers and divide by 2

Mode

Most

-which number occurs most often

Standard Deviation Steps

1. Calculate the mean of the data set

2. Calculate each variable (x) minus the mean. (x-x̄) (ie.subtract the mean from each value of the data set)

3. Square each value left over (square numbers from step 2)

4. Add them all together (add all the squares from step 3)

5. Divide by n-1 (for a sample; if it's population, just divide by n)

6. Take the square root

Bar Graphs

-Used for qualitative data

(qualities)

-graph showing the frequency of occurrence in each category for qualitative data

Histograms

-used by quantitative data

(numbers)

-graph showing the frequency of occurrence in each category for quantitative data

Time Series Analysis

-Generally involves trend, cycle, seasonal, and random factor analyses

-resulting set of data points taken over a specific interval

Scatter Plot

-typically quantitative data

-0 correlations =random blobs

-positive correlation: bottom left to top right, can easily draw trend line

-negative correlation: top left to bottom right

-graph used to compare two variables to determine if there is a possible relationship between them

Cyclical Trend

A pattern that tends to repeat itself every few years and is observed over a long period of tine

Population

entire set of data being evaluated

Pie Chart

Graph showing the percentage of occurrence in each category for qualitative data

Probability

Mathematical statement about the likelihood of an event occurring

Sample

Subset of the population

Trend

General upward or downward movement of data over a relatively long period of time

Random Trend

Unpredictable trend in data

Nonlinear Equation

An equation where the solution set does not form a straight line when it is plotted on a coordinate graph.

Uncertainty

A non-quantifiable value because the future events are not predictable

Decision Point

A point where one of several alternatives can be selected

-very specific, the decision maker has the exactly right information and has followed the decision making techniques, resulting in the final step of making a decision

-ie: the company can build small, medium, or large"

-a manufacturing firm is considering buying a larg or small plant

State of Nature

A possible outcome on a decision tree that would be out of the decision maker's control

- applied to an outcome, the probability represents the likelihood that an outcome will occur

-ie: "there is a 70% chance an expansion will cost the economy during upswing"

Risk

Known possibility measured by its probability of occurrence

Expected Monetary Value

Method used for decision making when the risks involved in a decision situation have several states of nature and the likelihood, or probability, of each state is known

Payoff Table

Similar to a decision tree except that is uses a table instead of a graphical representation of data

Decision Tree

Tool that can be used to visualize important aspects of a problem

The expected payoff

A calculated value, using a decision alternative's value and multiplying it by the probability will result in the expected pay off

-ie constructing a large factory in an expanding economy will likely realize a million profit in 3 years

-building a large factory in an expanding economy situation, the company estimates that is will realize a profit of 4.5 million in the first year

Decision Making Steps

1. Identifying the problem

2. Establish decision criteria

3. Weigh the decision criteria

4. Generate Alternatives

5. Evaluate the alternatives

6. Choose the best alternative

7. Implement the decision

8. Evaluate the decision

Decision Making: Step 1

Identify the problem

-focus on the problem not the symptoms, all parties agree to the problem statement

Decision Making: Step 2

Establish decision Criteria

-clearly state what is necessary to solve the problem, the requirements to meet

Decision Making: Step 3

Weigh the decision criteria

-need to equal 100%

Decision Making: Step 4

Generate Alternatives

-the list of choices your evaluating

Decision Making: Step 5

Evaluate the alternatives

-Rank the criteria for each alternative

Decision Making: Step 6

Choose the best alternative

-ranking/weight for each alternative, pick the best one

Decision Making: Step 7

Implement the decision

- do what you decided, ie sign the lease, relocate the building...

Decision Making: Step 8

Evaluate the decision

-what should you do different, what worked well

Decision under risk

Interest rates will start at 5%, will increase of 2% max every 3rd year depending on state of the economy at that time. overall cap is 11%

-the weather man is predicting snow during the nigh hours

Decision under certainty

-they know the exact risk and outcome

Decision Tree

a graph of decisions and their possible consequences; it is used to create a plan to reach a goal

Expected Value

-A weighted average of all possible outcomes with the weights being their probability of occurring

-the SUM of all possible outcomes multiplied by their probability occurrence

-used in decision tree, payoff and expected values models

- uses probabilty associated with different event outcomes

-for each option, multiply each event by its associated probability

-total up the SUM of the expected Value, select the options with the highest expected value

Expected Value Formula

E = ∑ [x • P(x)]

-multiply probabily times payoff, then add across the options such that probabilites add to 1 or 100%

Example of Expected Value

small building: strong sales are 10 million, weak sales are 2 million. Probability of strong sales is .75, weak is .25

10*.75= 7.5 million, 2 million *.25= .5 million

7.5 +.5= 8 million

8 million is the expected value of the small building

Project Characteristics

- creates a unique product or service, or event

-endeavor is outside of normal routine or operational activities

-assignment is temporary

-has a start and end date

-contains tasks that are specific to the objective or goal of the project

-all tasks must be done for it to be complete

examples: completing a degree program, cooking a meal, building a house

Project Planning Activities

- define the projects goals and objectives

-define the tasks required to complete the project

-define task dependencies and relationships )the order of tasks that they must be completed in)

-define the duration (completion time), the completion costs, and required resources (labor, material, etc)

-schedule, monitor, and control the project tasks as they are executed

Project Task

-activity, is a unique unit of the project which can be described within limits of time

-sequence must be done to establish task dependencies

-each task must be assigned a duration, or length of time required to complete the task

Predecessor

A task that must be completed before the next task can be started

Successor

Task that must follow another task

Defining Project Tasks

- common practice to start in a tabular format, and create columns for important information (identifier, description, predecessor, duration, assigned resources, cost)

-often start with the basic information (identifier, description) and add more information (predecessor, duration, costs...) as it becomes available

Project

A strategic undertaking and not a regular operational activity

Network Diagram

Identifiable set of project activities organized in a logical method

Optimistic Time

The best case scenario, or minimum length of time, to complete an activity

Most Likely Time

The duration of an activity given a normal level of effort and performance under normal working conditions

Critical Path

The longest sequence of tasks in the network diagram (duration not steps)

**the shortest amount of time in which a project can be complete

Pessimistic Time

The worst case scenario, or maximum length of time, to complete an activity

Network Diagram

-Identifies each task and provides a duration needed to complete the task

-help plan, manage, and monitor the project through the duration of the project

Steps for creating a network diagram

1. define the project and all of the project tasks

2. determine the task relationships and which activities must precede or succeed others

3. Draw the network diagram connecting activities

4. assign time estimates or duration to each activity

Beta Distribution estimating method

A powerful tools that helps predict project and activity duration while incorporating risk and uncertainty in the estimate

-AKA three point estimation

(most likely, optimistic, pessimistic)

-apply a program evaluation and review technique (PERT) that uses statistical distribution called beta distribution

Calculating Estimated Task Completion Times

Test= (A+(M*4)+p) / 6

Activity Cost Crashing

- crash the project with additional resources so the project can get done sooner

-only critical path activities can be crashed

-would choose the lowest crash cost per unti

-always adds expenses

Cost Crashing Formula

(Crash cost - Normal cost) / (normal duration- crashed duration)

Activity Node

Early Start Time: add ES to duration (forward pass)

Late Time (backward pass) latest start time minus the duration of the task

Linear Programming

A mathematical technique used to identify the value of a variable for a given set of constraints

-seeks to optimize a business value, usually minimizing costs and maximizing profits

Economic Ordering Quantity

Amount of inventory a business should order to minimize the total amount of inventory costs, including carrying, ordering, and shortage costs

-

Inventory

Any goods held in stock for immediate or future use

Feasible Region

Area of the graph that satisfies all constraints

Coefficient

Multiplier of the variable, as in linear equations or inequalities

Constraint

Restrictions that limit the degree in which a company can pursue its objective

-

Ordering Costs

The cost of replenishing inventory, including receiving logistics

Carrying Costs

The costs of storing inventory, insurance, and managing inventory risk due to damage or theft

Shortage Costs

The costs resulting from not having an item on the shelf for sale

Objective Function

The function that seeks to maximize or minimize some quantity -the problem to be optimized

(no equal sign... _x +_y)

Demand

The number of items needed, typically per year

Linear Programming problems for this course

- single criteria problems, only emphasizing maximization or minimization

-all equations and inequalities are linear

-all graphs are a continuous line

-all variables are non-negative. For a variable x, xi > or = 0

Formula for time duration

Test= (a +(m*4) + P) /6

Annual Holding Cost Formula

(average inventory level) * Holding cost per unit per year

Holding Cost= order quantity divided by 2 times holding cost