1. Name: Angelica F. White WEMBA10

2. Teach students how to make sound decisions and recommendations that are based on reliable quantitative information During this course students are introduced to the following tools to help with these analysis: Precision Tree Minitab

3. “ Because I said so…” “ And the data supports that …”

4. the best decision 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 decision assumptions Along 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 Sensitivity Analysis help us to analyze the accuracy of our assumptions

7. A 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 FullPopulationFullPopulation SampleSample Set of the population

8. Step I – Run Basic Statistics on Data

9. 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 Maximum Sales 12 0 2.375 0.151 0.522 1.400 1.975 2.500 2.775 3.100 Space 12 0 12.50 1.69 5.84 5.00 6.25 12.50 18.75 20.00 Place 12 0 0.333 0.142 0.492 0.000 0.000 0.000 1.000 1.000 Results for: Petfood(1).xlsx Descriptive Statistics: Sales, Space, Place Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Sales 12 0 2.375 0.151 0.522 1.400 1.975 2.500 2.775 3.100 Space 12 0 12.50 1.69 5.84 5.00 6.25 12.50 18.75 20.00 Place 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.data setstandard deviation 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

10. Step II – Review Basic Statistics Results

11. Step III – Identify Correlation Among Data Variables

12. Step IV – Review Correlation Results Correlations: Sales, Space, Place Sales Space Space 0.827 0.001 Place 0.424 0.000 0.169 1.000 Correlations: Sales, Space, Place Sales Space Space 0.827 0.001 Place 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  Scatterplot Covariance Test is used to measure how much two variables change together

13. 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).dependent variableindependent variables 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 is Sales = 1.30 + 0.0740 Space + 0.450 Place

14. 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

15. Step IV – Review Regression Results Regression Analysis: Sales versus Space, Place The regression equation is Sales = 1.30 + 0.0740 Space + 0.450 Place Predictor Coef SE Coef T P Constant 1.3000 0.1569 8.29 0.000 Space 0.07400 0.01101.72 0.000 Place 0.4500 0.1305 3.45 0.007 S = 0.213177 R-Sq = 86.4% R-Sq(adj) = 83.4% Analysis of Variance Source DF SS MS F P Regression 2 2.5935 1.2967 28.53 0.000 Residual Error 9 0.4090 0.0454 Total 11 3.0025 Source DF Seq SS Space 1 2.0535 Place 1 0.5400 Regression Analysis: Sales versus Space, Place The regression equation is Sales = 1.30 + 0.0740 Space + 0.450 Place Predictor Coef SE Coef T P Constant 1.3000 0.1569 8.29 0.000 Space 0.07400 0.01101.72 0.000 Place 0.4500 0.1305 3.45 0.007 S = 0.213177 R-Sq = 86.4% R-Sq(adj) = 83.4% Analysis of Variance Source DF SS MS F P Regression 2 2.5935 1.2967 28.53 0.000 Residual Error 9 0.4090 0.0454 Total 11 3.0025 Source DF Seq SS Space 1 2.0535 Place 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/SeCoef P = 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.

16. 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

17. Step IV – Arriving at the Best Regression Model Select new set variables Run Regression Review results for 1. Variables fit 2. Variability strength 3. Inexistence of hidden correlations Best Model? Variables with P < 0.05 and T > 2.0 and R-Sq > 50% BEST MODEL NO YES

18. 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 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.

19. 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.statisticsdispersionpopulationprobability distributionmean 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.confidence in statistical conclusionsmargin of errorpollingnormal distribution In addition to expressing the deviation, the radius of a 95% confidence interval.)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.sciencestatistically significantfinancerate of returninvestment risk A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data.variance 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 Wikipediasample