Supplementary Notes on Regression _Dr. Walker_

Supplementary Notes on Regression _Dr. Walker_ - ITIS 1P97...

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ITIS 1P97 Dr. John Walker Page 1 of 8 Pages REGRESSION ANALYSIS Definition: Regression analysis, one of the most useful quantitative tools for business and economic analysis due to its wide applicability, is the study of relationships between variables. Some examples include: Variation of wages/salaries of employees vs. years of experience, education levels, and gender. Change of the current price of a stock vs. its own previous prices, and the current and previous prices of a market index. A firm’s current sales level vs. its current and past advertising levels, its own past sales levels, its competitors’ advertising levels, and the general market condition. The selling price of a house vs. the appraised value of the house, the size (ft ) of the house, the property size, and the number of bedrooms, etc. Classifications of Regression Analysis: (1) Based on the purpose of the analysis: To understand what has happened To make a prediction or a forecast (2) Based on the type of data analyzed: Cross-sectional data – data gathered from approximately the same period of time e.g. smoking vs. lung cancer; sales levels vs. advertising expenses, etc. Time series data – one or more variables observed at several, but equally spaced, points in time e.g. Canadian population over past 20 years; sales levels over past 36 months (3) Based on the number of explanatory (independent) variables Simple regression – only one explanatory (independent) variable Multiple regression – two or more explanatory (independent) variables (4) Based on the type of the relationships Linear regression – a linear relationship between the dependent variable and the explanatory (independent) variables Nonlinear regression – relationship other than linear (e.g., quadratic, log linear, etc.) Correlations Numerical measures (between 0 and 1) that indicate the strength of linear relationships between pair of variables. Relevant to only linear relationships. Correlation 0 no linear relationship Correlation 1 → strong positive linear relationship Correlation -1 → strong negative linear relationship
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ITIS 1P97 Dr. John Walker Page 2 of 8 Pages SIMPLE LINEAR REGRESSION Least Squares Estimation (line) The best fitted line that minimizes the sum of the squared errors (residuals). bX a Y ˆ where 2 X X Y Y X X b i i i and a = X b Y Fitted Value – the predicted value of the dependent variable, which is determined by the regression line. Residual (Error) – the difference between the actual and fitted values of the dependent variable, note this is given by ii Y -Y ˆ for a given data point i. Correlation Coefficient (R) – the correlation between the fitted values and the observed values of the dependent variable.
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This note was uploaded on 11/04/2011 for the course ITIS ITIS1p97 taught by Professor Dr.susansproule during the Fall '11 term at Brock University, Canada.

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Supplementary Notes on Regression _Dr. Walker_ - ITIS 1P97...

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