Managing As If Numbers MatterBUS.550E

Course Overview

Name: Angelica F. White

WEMBA10

Objective

Teach students how to make sound decisions and recommendations that are based on reliable quantitative informationDuring this course students are introduced to the following tools to help with these analysis:

Precision Tree

Minitab

Supporting your Recommendation

“ Because I said so…”

From:

To:

“ And the data supports that …”

Precision Tree Analysis

A tool that helps with the analysis of all options available in a decision, identification of their Estimated Monetary Value (EMV) and realization of the optimum EMV value – the best decisionAlong the decision process various assumptions are made, these assumptions are the base of your decision model and its accuracy relevant to the reliability of your decision. Sensitivity Analysis help us to analyze the accuracy of our assumptions

Precision Tree

Sensitivity Analysis

MinitabA statistical tool that helps with the analysis of the data relevant to my decision or recommendation.The tool provides statistics, correlation, trend and predictability results based on a data set.

The data set used can be a SAMPLE data or a FULL POPULATION data

FullPopulatio

n

Sample

Set of the

population

Steps to Analyze DataStep I – Run Basic Statistics on Data

Step II – Review Basic Statistics Results

Results for: Petfood(1).xlsx

Descriptive Statistics: Sales, Space, Place

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 MaximumSales 12 0 2.375 0.151 0.522 1.400 1.975 2.500 2.775 3.100Space 12 0 12.50 1.69 5.84 5.00 6.25 12.50 18.75 20.00Place 12 0 0.333 0.142 0.492 0.000 0.000 0.000 1.000 1.000

N – Number of items in your data set

N* - Number of items with error in your data set

Mean - For a data set, the mean is the sum of the observations divided by the number of observations. The mean is often quoted along with the standard deviation: the mean describes the central location of the data, and the standard deviation describes the spread. SE Mean – Standard Error of the Mean

StDev – Standard Deviation

Minimum – The smallest value in the data set

Maximum – The greatest value in the data set

Median - The average value of your data set

Step II – Review Basic Statistics Results

Step III – Identify Correlation Among Data Variables

Step IV – Review Correlation Results

Correlations: Sales, Space, Place

Sales SpaceSpace 0.827 0.001Place 0.424 0.000 0.169 1.000

Correlation, is a linear relationship, is also defined as the measure of how much two variables relates to each other.The greatest is the number the stronger is the correlation. Ex: Space and Sales have the strongest correlation among these variables

Scatterplot graphs also can help visualize the existence or non of correlation. Menu: Graph ScatterplotCovariance Test is used to measure how much two variables change together

Step V – Run Regression Test

In statistics, regression analysis refers to techniques for the modeling and analysis of numerical data consisting of values of a dependent variable (also called response variable or measurement. Ex Sales) and of one or more independent variables (also known as explanatory variables or predictors. Ex: Space & Place). The dependent variable -Sales in the regression equation is modeled as a function of the independent variables selected, the one with significant correlation.We execute Regression test to generate Prediction, Inference, Hypothesis Testing And Modeling of Casual relationships. Menu: Stat Regression Regression

Dependent Variable

Independent Variables

The regression equation isSales = 1.30 + 0.0740 Space + 0.450 Place

Step V – Run Regression Test

While correlation test allows you to identify and measure the linear relationships among variables, regression test allows you to analyze the interdependency of these relationships from different angles.

Sales

Space

Place

Step IV – Review Regression Results

Regression Analysis: Sales versus Space, Place

The regression equation isSales = 1.30 + 0.0740 Space + 0.450 Place

Predictor Coef SE Coef T PConstant 1.3000 0.1569 8.29 0.000Space 0.07400 0.01101 .72 0.000Place 0.4500 0.1305 3.45 0.007

S = 0.213177 R-Sq = 86.4% R-Sq(adj) = 83.4%

Analysis of VarianceSource DF SS MS F PRegression 2 2.5935 1.2967 28.53 0.000Residual Error 9 0.4090 0.0454Total 11 3.0025

Source DF Seq SSSpace 1 2.0535Place 1 0.5400

An example the regression equation use , is that it can be applied to predict sales volume taking in consideration the degree that each variables influence sales.Lets understand the results:Coef = Is the value of my model, identified for each variable, that is not affected by variation.SE Coef = Standard Error of Coef T= Is the mean for the sample population. T=Coef/SeCoefP = Degree of random numbers in my module. P closer to 0 shows a stronger module.S = Standard Deviation

Large gaps among R variables indicates that some variables are not so strong for analysis.

Step IV – Review Regression Results

Review P and T values for variables• P < 0.05, closer to zero, indicates a stronger fit AND• T > 2 , reinforces the variable fit to the function

How strong is the relationship among selected variables in my function?• When it shows large percents of R variable AND• Small gaps among R variables .

Review the residuals• Exam the residual graphs and look for structure. The inexistence of it is a good sign• Exam residual plots for normal distribution, maybe the existence of a hidden data correlation

Finalizing your review• You may decide to remove weak variables from your function• You may want to add other variables to strengthen the model, increase R value• Run regression for the selected variables

Step IV – Arriving at the Best Regression Model

Select new set variables

Run Regression

Best Model?Variables with P

< 0.05 and T > 2.0 and

R-Sq > 50%

BEST MODEL

NO

YES

Step V – Presenting your Analysis

After several iterations of regression analysis, you may decide that the current model is reliable when:

• Selected variables have a P value < 0.5 and T value > 2.0• When R-Sq and R-Sq(adj) values are high and there is minimum gap among

them. Now you need to present this information in the way your target audience can understand it. Use graphs and pictures to demonstrate the results. In our example Place has little impact on sales volume, reversely Space above 50 can exponentially increase sales volume.

Sales Place=1 Sales

Place=0

05

10152025

Space -10Space -50

Space - 100

Space -10Space -50Space - 100

In statistics, standard deviation is a simple measure of the variability or dispersion of a population, a data set, or a probability distribution. A low standard deviation indicates that the data points tend to be very close to the same value (the mean), while high standard deviation indicates that the data are “spread out” over a large range of values.

For example, the average height for adult variability of a population, standard deviation is commonly used to measure confidence in statistical conclusions. For example, the margin of error in polling data is determined by calculating the expected standard deviation in the results if the same poll were to be conducted multiple times. (Typically the reported margin of error is about twice the standard deviation men in the United States is about 70 inches, with a standard deviation of around 3 inches. This means that most men (about 68%, assuming a normal distribution) have a height within 3 inches of the mean (67 inches – 73 inches), while almost all men (about 95%) have a height within 6 inches of the mean (64 inches – 76 inches). If the standard deviation were zero, then all men would be exactly 70 inches high. If the standard deviation were 20 inches, then men would have much more variable heights, with a typical range of about 50 to 90 inches.In addition to expressing the deviation, the radius of a 95% confidence interval.)

In science, researchers commonly report the standard deviation of experimental data, and only effects that fall far outside the range of standard deviation are considered statistically significant. Standard deviation is also important in finance, where the standard deviation on the rate of return on an investment is a measure of the risk.

A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data.When only a sample of data from a population is available, the population standard deviation can be estimated by a modified standard deviation of the sample. Source Wikipedia

Standard Deviation - Sigma