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PPT6 Multiple Regression0 - McGill University Advanced...

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McGill University Advanced Business Statistics MGSC-272
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Fall’07 Multiple Regression Read: A Second Course in Statistics , William Mendenhall/Terry Sincich, 6 th edition Chapter 5
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Multiple Regression
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Cross Sectional vs Time Series There are two types of financial/econometric studies depending on the phenomenon to be explained: cross-sectional longitudinal (time-series). Typically, a financial study might be made of a number of companies or their common stocks and their earnings and other annual financial data and market data for a number of consecutive months or years.
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Examples of cross-sectional and times studies A cross-sectional study would include multiple companies or stocks for any one time period, such as 1999, to account for variation in some factor of interest across all the companies at that time. A longitudinal or time-series study would include multiple time periods for any one company, such as Yahoo, Inc., to account for changes in some factor of interest over all the time periods for that company .
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Combination Studies A combination cross-sectional and longitudinal study can be made to address both dimensions of change, space and time. For example, a panel study would include all of the data items for the same identical companies for the same identical number of time periods, such as all the companies in the S&P 500 Index at the end of 1999 for the months or years from January 1990 through December 1999.
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Multiple Regression Multiple regression is regression analysis with more than one independent variable. True Regression Equation: E(Y) = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + ..... + β K X K Estimated Regression Equation: = b 0 + b 1 X 1 + b 2 X 2 + b 3 X 3 + ..... + b K X K ˆ Y
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The Model Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + ..... + β K X K + where = independent N(0, 2 ) Note that this model assumes: (1) Normality (2) Homoscedasticity (equal variances) (3) independence
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Definition of Terms X K = the independent variables. β K = the true regression parameters. b K = the estimated regression coefficients ε = the error term. b K = the change in Y (the dependent variable) per unit increase in X K with all other independent variables held fixed.
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EXAMPLE The VP Sales decides to attempt to construct a regression model which will explain a higher percentage of the variation in store profits. The dependent (response) variable is profit in $1,000 per day. A brainstorming session with middle-management results in the following set of potential explanatory (predictor) variables. X 1 = Advertising expenditure per month in $1,000 (ADVERT). X 2 = The number of in-store specials offered per day (SPECIAL). X 3 = The size of the store in thousands of square feet (SIZE). X 4 = The location of the store (PLACE). where X 4 = 0 if the store is in Toronto, 1 if the store is in Montreal Note: X 4 is called a dummy or indicator variable.
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Data Y X 1 X 2 X 3 X 4 STORE PROFIT ADVERT SPECIAL SIZE PLACE 1 9.4 3 1 30 1 2 10.3 3 5 37 1 3 10.9 4 5 38 1 4 9.9 4 2 35 1 5 12.9 5 6 40 0 6 11.8 5 6 40 0 7 11.5 6 2 39 1 8 13.2 6 5 45 0 9 12.8 7 5 41 0 10 12.1 7 1 41 0
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Correlation Matrix Profit Advert Special Size Place Profit 1 Advert .8056 1 Special .5037 0 1 Size .9145 .7577 .5014 1 Place -.8604 -.7071 -.4126 -.7318 1 This is good!
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