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Real Estate Modelling and Forecasting by Chris Brooks and Sotiris Tsolacos_4

Tham khảo tài liệu 'real estate modelling and forecasting by chris brooks and sotiris tsolacos_4', tài chính - ngân hàng, đầu tư bất động sản phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | An overview of regression analysis 107 A term in 2xt can be cancelled from the numerator and denominator of 4A.29 and recalling that x xt x this gives the variance of the slope coefficient as s 2 var 3 ------ 4A.30 y xt x 2 so that the standard error can be obtained by taking the square root of 4A.30 Si SE P s 1 y xt x 4A.31 Turning now to the derivation of the intercept standard error this is much more difficult than that of the slope standard error. In fact both are very much easier using matrix algebra as shown in the following chapter. This derivation is therefore offered in summary form. It is possible to express a as a function of the true a and of the disturbances ut E u E x2 A I a a xt y x r E x2 4 E xộ2 4A.32 Denoting all the elements in square brackets as gt 4A.32 can be written a a y utgt From 4A.15 the intercept variance would be written var a E UtgẦ y g2E u2 s 2y g2 tt t t t Writing 4A.34 out in full for gt2 and expanding the brackets 22 22 2 2 s I Í I x. I 2 xt I x. I xt I I xt II xt I I var a I y J r E x2 E xộ 4A.33 4A.34 4A.35 This looks rather complex but fortunately if we take xt2 outside the square brackets in the numerator the remaining numerator cancels with a term in the denominator to leave the required result SE a s xt2 T y xt xý 4A.36 5__ Further issues in regression analysis Learning outcomes In this chapter you will learn how to construct models with more than one explanatory variable derive the OLS parameter and standard error estimators in the multiple regression context determine how well the model fits the data understand the principles of nested and non-nested models test multiple hypotheses using an F-test form restricted regressions and test for omitted and redundant variables. 5.1 Generalising the simple model to multiple linear regression Previously a model of the following form has been used yt a fat Ut t 1 2 . T 5.1 Equation 5.1 is a simple bivariate regression model. That is changes in the .