Regression

# Regression - Regression Regression is a technique used to analyze the relationship between a dependent(criterion variable and one or more

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Regression Regression Regression is a technique used to analyze the relationship between a dependent (criterion) variable and one or more independent (predictor) variables We need an interval dependent variable and either interval or binary independent variables. (i.e. we predict or explain Y with one or more X's)

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What’s the Purpose? What’s the Purpose? 1. Predict the dependent variable for a new set of data. 2. Assess the explanatory power of the independent variable(s). 3. Identify the subset of measures that is most effective for predicting the DV. 3 Reasons to Fit a Regression Model:
Regression equation: Υ = b o + b 1 x 1 + b 2 x 2 + … ε where: b o is the intercept (a.k.a. the constant) b n are the regression coefficients ε is the residual - difference b/t the observed values and the values predicted by the model = true error Regression Regression

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So what do the different parts of the equation tell you? Intercept/Constant : tells you (1) where the regression line crosses the Y axis and (2) the value of Y when the IVs are equal to 0 Regression coefficients: tell you (1) the slope of the regression line and (2) how much the dependent variable is expected to increase when that particular independent variable increases by one, holding all the other independent variables constant. Regression Regression
IV Sales = DV 0 20 40 60 80 80 60 40 20 b o slope= b 1 Σ = ε regression line (predicted) Y - observed Regression Regression

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Salespeople Sales = DV 0 2 4 6 8 10 400 300 200 100 500 regression line (predicted) Predicting with Regression: Predicting with Regression: Given the 2 to 1 linear relationship, we can accurately predict sales.
Regression is related to statistics that we have discussed at length Correlation - measure of the covariation between variables. varies between -1 and +1 so r = +1 means that the variables are perfectly positively correlated Regression Regression

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Q: How Are Correlation and Regression Related?? A: The square of the correlation is R 2 - gives the explained variance of the dependent variable by the independent variable(s) - called the coefficient of determination (R 2 ) So, regression is a linear relationship which depicts the way two or more variables covary.
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## This note was uploaded on 06/23/2011 for the course MKTG 352 taught by Professor ? during the Summer '10 term at South Carolina.

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Regression - Regression Regression is a technique used to analyze the relationship between a dependent(criterion variable and one or more

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