G3e03 - Chapter 3 Multiple regression analysis Overview...

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Chapter 3 Multiple regression analysis Overview This chapter introduces regression models with more than one explanatory variable. Specific topics are treated with reference to a model with just two explanatory variables, but most of the concepts and results apply straightforwardly to more general models. The chapter begins by showing how the least squares principle is employed to derive the expressions for the regression coefficients and how the coefficients should be interpreted. It continues with a discussion of the precision of the regression coefficients and tests of hypotheses relating to them. Next comes multicollinearity, the problem of discriminating between the effects of individual explanatory variables when they are closely related. The chapter concludes with a discussion of F tests of the joint explanatory power of the explanatory variables or subsets of them, and shows how a t test can be thought of as a marginal F test. Learning outcomes After working through the corresponding chapter in the text, studying the corresponding slideshows, and doing the starred exercises in the text and the additional exercises in this guide, you should be able to explain: the principles behind the derivation of multiple regression coefficients (but you are not expected to learn the expressions for them or to be able to reproduce the mathematical proofs) how to interpret the regression coefficients the Frisch–Waugh–Lovell graphical representation of the relationship between the dependent variable and one explanatory variable, controlling for the influence of the other explanatory variables the properties of the multiple regression coefficients what factors determine the population variance of the regression coefficients what is meant by multicollinearity what measures may be appropriate for alleviating multicollinearity what is meant by a linear restriction the F test of the joint explanatory power of the explanatory variables the F test of the explanatory power of a group of explanatory variables why t tests on the slope coefficients are equivalent to marginal F tests. You should know the expression for the population variance of a slope coefficient in a multiple regression model with two explanatory variables. 10.10.07
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2 Additional exercises A3.1 The output shows the result of regressing FDHO , expenditure on food consumed at home, on EXP , total household expenditure, and SIZE , number of persons in the household, using the CES data set. Provide an interpretation of the regression coefficients and perform appropriate tests. . reg FDHO EXP SIZE if FDHO>0 Source | SS df MS Number of obs = 868 -------------+------------------------------ F( 2, 865) = 426.78 Model | 1.4826e+09 2 741314291 Prob > F = 0.0000 Residual | 1.5025e+09 865 1736978.64 R-squared = 0.4967 -------------+------------------------------ Adj R-squared = 0.4955 Total | 2.9851e+09 867 3443039.33 Root MSE = 1317.9 ------------------------------------------------------------------------------ FDHO | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- EXP | .0372621 .0024547 15.18 0.000 .0324442 .04208 SIZE | 559.7692 30.85684 18.14 0.000 499.2061 620.3322 _cons | 884.5901 100.1537 8.83 0.000 688.0173 1081.163 ------------------------------------------------------------------------------ A3.2 Perform a regression parallel to that in Exercise A3.1 for your CES category of expenditure, provide an interpretation of the regression coefficients and perform appropriate tests.
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G3e03 - Chapter 3 Multiple regression analysis Overview...

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