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211-01-2+Class+Notes+3-1 - DSC 211 CLASS NOTES 3-1...

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DSC 211 CLASS NOTES 3-1 INVESTIGATION OF RELATIONSHIPS AMONG PROPERTIES (VARIABLES) OVERVIEW: In this last module, we will study "possible relationships" among properties of some population. For example, based on a sample Issue: Some business population (all our employees) and two or more properties/variables for the property we'd like to be able to predict or understand -- if we knew values for the x's (independent variables). Three (A) Does the sample provide evidence that a relationship exists among y, x1, x2, …? For Example: Business In this question, note that we must hypothesize a specific form, e.g., a linear or quadratic relationship. Questions: question. And often, a final business question is the following: provide sufficient evidence that (C ) If yes to (A) and (B), what is an estimate (with margin of error) for mean y, E(y), for given values of x's? a relationship exists. Data: in the sample data accounted for by the relationship. Analysis: REGRESSION ANALYSIS -- 4 STEPS -- Given hypothesized model and sample data Using the sample data, develop estimates for the intercept and all coefficients of a possible relationship. How strong is the fit of the sample data to the model? -- 2 measures. Statistically, can we say that the sample provides strong, or very strong, evidence that a relationship exists? -- Hypothesis tests Using the sample data, can we conclude that four required conditions hold? Answers: Provide, in business language, the best answers to the questions above. Class Notes 3 -1 will introduce regression analysis for the most basic relationship between two variables. the 4 steps of analysis -- plus examples. Can weight be predicted by height for (all) 12 year olds? If we obtained a sample of 12 year olds, how would we investigate that question? The general name for the analysis we will study is REGRESSION ANALYSIS . For this course, we will always use the following BFDA and the 4 steps of regression analysis: of the members of the population. We'll use symbols y, x 1 , x 2 , … The symbol y (dependent variable) is used Population: All our sales people For example, we might hypothesize: y = annual sales ($) y = beta(o) + beta(1) * x 1 + beta(2) * x 2 + e. x 1 = sales aptitude score where the beta's are constants and e stands for all other random error we cannot predict with x 1 and x 2 . x 2 = district 1, 2, or 3 (B) If yes to (A), how "strong" and "significant" is the relationship? Not always stated but always an implied Significant -- sample results Strength -- amount of variation A sample of size n of values of y, x 1 , x 2 , … 1. Estimate the model (the relationship). such as: y = 10.25 + 0.55 * x 1 - 6.00 * x 2 . 2. Assess the estimated model . 3. Check the required conditions (of regression analysis) -- FOUR CONDITIONS. 4. Estimate mean y for given values of the x's . If 2 and 3 provide good results, Develop a single estimate for mean y and a margin of error -- since all this is based on a sample.
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